Device for measuring physiological state

ABSTRACT

A non-invasive device for evaluating circulatory state parameters, and specifically, a pulsewave analysis device capable of evaluation by separating blood vessel compliance and blood vessel resistance into central and peripheral components of the arterial system is provided. Microcomputer  4  detects the waveform at a test subject&#39;s radius artery via pulsewave detector  1,  and uptakes the stroke volume in the test subject which is measured by a stroke-volume measurer. Next, based on the measured stroke volume, microcomputer  4  adjusts the values of each element in a lumped five parameter model made up of an electrical circuit which models the arterial system from the center to the periphery of the body, so that the response waveform obtained when an electric signal corresponding to the pressure waveform at the proximal portion of the aorta in a test subject is provided to the electric circuit coincides with the waveform at the radius artery. Microcomputer  4  then outputs the thus-obtained values of each element as circulatory state parameters. In addition, microcomputer  4  calculates the diastolic pressure value, systolic pressure value and pulse waveform at the proximal portion of the aorta from the values of each element, and outputs the calculated result to output device  6.

This application is a continuation of Ser. No. 08/860,579 filed Jul. 24,1997, which is a 371 of PCT/JP96/03211 filed Nov. 1, 1996, the entirecontents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optimal device for measuringphysiological state which is used to measure conditions in the humanbody. More specifically, the present invention relates to a device foranalyzing pulse waves used to diagnose the circulatory system in thehuman body, and to a sphygmomanometer which evaluates compliance andresistance in the blood vessels at the center and periphery of thecirculatory system based on the physiological state measured at theperiphery of the human body, and estimates blood pressure at the centerof the circulatory system.

2. Background Art

Blood pressure and heart rate are most commonly used when diagnosing thecondition of the circulatory system in the human body. However, in orderto carry out a more detailed diagnosis, it becomes necessary to measurethe so-called circulatory state parameters of compliance and viscousresistance in the blood vessels. Moreover, in the case where theseparameters are expressed using a model, a lumped four parameter modelmay be employed as a model for expressing the behavior of the arterialsystem.

The pressure waveform and blood flow volume at the proximal portion ofthe aorta and at the site of insertion of a catheter into an artery needto be measured in order to measure these circulatory state parameters,however. For this purpose, a direct method of measurement, in which acatheter is inserted into an artery, or an indirect method employingsupersonic waves or the like, may be applied. However, the former methodis invasive, and employs a large device, while the latter method,although permitting non-invasive observation of blood flow within theblood vessels, requires training and, moreover, necessitates a largedevice to carry out the measurements.

Accordingly, the present inventors discovered a method for approximatingthe parameters in a lumped four parameter model by measuring just thepulse waveform at the radius artery and the stroke volume. Thereafter,the present inventors proposed a pulsewave analysis device capable ofcarrying out an evaluation of the circulatory state parameters in aneasy and non-invasive method by employing this method (see JapanesePatent Laid-open Publication No. Hei 6-205747, Title: Device forAnalyzing Pulsewaves).

However, the aforementioned method does not employ a model which treatsblood vessel compliance at the periphery and center of the arterialsystem separately. Accordingly, when exercising, or in cases where apharmacological agent effecting circulatory state has been administeredto a patient, it is not possible to evaluate the separate effects ofthat medication at the periphery and center of the arterial system.

A brief explanation will now be made of the aforementioned measurementof blood pressure.

In the non-invasive sphygmomanometer conventionally employed, a cuff isattached to the upper arm, for example, of a test subject, pressure isapplied to the cuff and the pulsewave of the test subject is detected toprovide a measurement of blood pressure. Japanese Patent ApplicationLaid Open No. Hei 4-276234, for example, discloses a sphygmomanometer atthe periphery of a test subject's body. Namely, as shown in FIG. 29,cuff 110 is wrapped around the upper arm of a test subject, and a band138 is wrapped around the subject's wrist 140. Pulsewave sensor 134 isattached to the radius artery of the test subject, and the testsubject's pulsewave is detected. After applying pressure to cuff 110,the conventional oscillometric method is employed to measure thesystolic and diastolic pressure values as the pressure falls.

However, if blood pressure values at the periphery and center of thearterial system in the human body are actually measured, a difference incenter and peripheral blood pressure values is observed, particularly inthe case of the systolic pressure value. Moreover, the degree of thisdifference varies depending on the shape of the pulsewave which isobserved at the periphery of the arterial system. FIGS. 22 through 24are provided to explain this variation in blood pressure valuesaccording to pulsewave shape. The pressure waveform andsystolic/diastolic pressure values at the aorta, which is at the centerof the arterial system, and the pressure waveform and systolic/diastolicpressure values at the radius artery, which is at the periphery of thearterial system, are shown in these figures.

FIG. 22 shows the first type of pulse waveform, wherein the systolicpressure value obtained at the aorta is indicated by the dashed line andthe systolic pressure value obtained from the radius artery is indicatedby the solid line. Although the systolic pressure value obtained at theradius artery is slightly higher, these blood pressure values may beviewed as almost equivalent. In the case of the second type of pulsewaveform shown in FIG. 23, however, the difference between the systolicpressure values obtained at the aorta and at the radius artery is 14.9mmHg, a considerably greater difference than observed in the case of theType I pulse waveform shown in FIG. 22. Further, in the case of thethird type of pulse waveform shown in FIG. 24, the difference betweenthe systolic pressure values is even greater, at 26.1 mmHg. Moreover, incontrast to the Type I and Type II pulse waveforms, in the case of aType III pulse waveform, the pressure waveform obtained at the aorta ishigher in its entirety than that of the pressure waveform obtained atthe radius artery. Thus, based on these figures, the diastolic pressurevalue at the radius artery does not depend on the shape of thepulsewave, but is approximately the same for each pulsewave type.

A brief explanation will now be made of the Type I, Type II and Type IIIpulsewaves described above. A Type I pulse waveform is observed in aperson of normal health. The waveform is relaxed and loose, and ischaracterized by a fixed rhythm with little disruption. On the otherhand, a Type II pulse waveform demonstrates a sharp rise followedimmediately by a fall. The aortic notch is deep, while the subsequentpeaks in the expansion phase are significantly higher than usual. A TypeIII pulse waveform rises sharply, with blood pressure remaining elevatedfor a fixed period of time thereafter, rather than immediately fallingoff.

As may be gathered from these figures, it is possible for the peripheralblood pressure value obtained at the radius artery or upper arm to beelevated, while the blood pressure value obtained at the proximalportion of the aorta, i.e., at the center of the arterial system, islow. Further, the opposite situation is also possible, namely, the bloodpressure value at the periphery is low, while the blood pressure valueat the center of the arterial system is high. This relationship willdiffer depending on the shape of the pulse waveform, and, moreover, isrealistically expressed in the shape of the pulse waveform.

For example, when a hypertensive agent is administered to a patient as atreatment for high blood pressure, the drug's effect is observed basedon the blood pressure at the radius artery. In this case, however, it ispossible that the blood pressure at the center of the arterial system isnot actually reduced, even if there is a drop in the blood pressurevalue measured at the periphery. Accordingly, it can be difficult tocorrectly ascertain the drug's effect based only on the peripheral bloodpressure value. Conversely, even if no change is observed in the bloodpressure at the periphery of the arterial system, the actual load on theheart may in fact have been reduced if there is a change in the pressurewaveform at the aorta, and the blood pressure at the center of thearterial system drops. In this case, the drug's effect has been fullyexpressed, even though there was no reduction in blood pressure at theperiphery of the arterial system. Accordingly, it is difficult todetermine this fact based only on the blood pressure at the periphery ofthe arterial system.

Accordingly, when measuring blood pressure, the correct approach is toobserve the extent of the actual load on the heart. This is because whena determination is made based on blood pressure values measured at theperiphery of the arterial system, as has been the conventional practice,there is a chance that the load on the heart will be over or underevaluated.

DISCLOSURE OF THE INVENTION

The present invention was conceived in consideration of the abovecircumstances, and has as its first objective the provision of a devicecapable of evaluating circulatory state parameters in a non-invasivemethod, and more particularly, to the provision of a device foranalyzing pulse waves that is capable of evaluating compliance andresistance in blood vessels at the center and periphery of the arterialsystem separately.

Further, the present invention's second objective in the provision of asphygmomanometer capable of obtaining the blood pressure value at thecenter of the arterial system from pulse waveforms measured at theperiphery of the arterial system.

The first standpoint of the present invention is characterized in theprovision of a measuring means for measuring physiological state, and ananalyzing means for calculating circulatory state parameters, includingthe viscoelasticity of the aorta, as circulatory state parameters whichshow the circulatory state of an organism's arterial system from thecenter to the periphery thereof, based on the physiological state of theorganism.

Thus, since circulatory state parameters, including viscoelasticity atthe aorta, in the arterial system of an organism are calculated, it ispossible to achieve a more precise evaluation since the circulatorystate of the arterial system, which extends from the center to theperiphery of the organism's body, is separated into a center componentand a periphery component.

In one embodiment of the present invention, circulatory state parametersare determined by approximating the aforementioned circulatory stateparameters in the organism's arterial system with an electric circuitbased on a lumped five parameter model. As a result, it is possible tomore easily calculate the circulatory state parameters conforming toconditions in the human body, as compared to a lumped four parametermodel.

In another embodiment of the present invention, the pulse wave at theperiphery of the arterial system is employed as the physiological state,the pressure waveform at the left cardiac ventricle in the body isprovided to a lumped five parameter model, and each of the elementsmaking up the lumped five parameter model is determined so as to obtainthe pulse waveform at that time. As a result, it is possible todetermine circulatory state parameters which closely match the pulsewaveat the periphery which was actually measured from the body.

In another embodiment of the present invention, an electric signalcorresponding to the pressure in the left cardiac ventricle isapproximated by a sinusoidal wave. Thus, it is possible to determinecirculatory state parameters which even more accurately express currentconditions at the center the arterial system in the body.

The second standpoint of the present invention is characterized inprovision of a measuring means for measuring physiological state at theperiphery of the arterial system, and a blood pressure calculating meansfor determining circulatory state parameters showing the circulatorystate in the arterial system based on physiological state, andcalculating the pressure waveform at the aorta based on theaforementioned circulatory state parameters.

Since the present invention calculates the pressure waveform at theaorta from the physiological state at the periphery of the arterialsystem in this way, the blood pressure value at the aorta can beestimated using just conditions at the periphery of the arterial system.As a result, there is no concern that a false conclusion will bereached, such as deciding that an administered pharmacological agent hadno effect because no change was observed in blood pressure measured atthe periphery. Thus, it becomes possible tow correctly ascertain theeffect of an administered pharmacological agent, making the presentinvention extremely useful when selecting drugs such as hypertensiveagents and the like.

Further, since one embodiment of the present invention provides thatparameters including viscoelasticity at the aorta are selected ascirculatory state parameters, it is possible to make an evaluation ofthe circulatory state at the center and at the periphery of the arterialsystem separately. As a result, an even more accurate estimation ofblood pressure is possible.

Moreover, another embodiment of the present invention provides thatcirculatory state parameters are determined by approximating thecirculatory state of the arterial system using an electric circuit basedon a lumped five parameter model. Therefore, it is possible to obtainthe blood pressure value at the aorta which more closely conforms withconditions in the human body.

Another embodiment of the present invention employs the pulsewave at theperiphery of the arterial system as the physiological state, providesthe pressure waveform at the left cardiac ventricle to a lumped fiveparameter model, and determines each element making up the model so asto obtain the pulsewave at this time. As a result, it is possible todetermine blood pressure at the aorta using circulatory state parameterswhich closely match the pulsewave at the periphery which is actuallymeasured in the body.

In another embodiment of the present invention, blood pressure at theaorta is estimated by determining circulatory state parameters withoutdetecting stroke volume. Thus, blood pressure measurements can be madewithout causing the test subject any unpleasant discomfort orinconvenience.

In another embodiment of the present invention, the values of thecirculatory state parameters are adjusted so that the calculated valueof stroke volume which is obtained from the pressure waveform of theaorta is equal to the actual measure value of the stroke volume which isobtained from the body. Thus, it is possible to even more preciselyestimate blood pressure at the aorta.

In another embodiment of the present invention, the workload on theheart is calculated based on the pressure waveform at the aorta. Thus,even when no notable change is observed in the blood pressure valueobtained at the periphery of the arterial system, it is possible toquantitatively indicate the actual load on the heart. Accordingly, it ispossible to carry out an even more exact evaluation of a treatmentmethod employing a hypertensive agent, for example.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a block diagram showing the structure of a pulsewave analysisdevice according to one embodiment of the present invention.

FIG. 2 is a diagram showing the conditions under which measurementsemploying a pulsewave detector 1 and a stroke-volume measurer 2 wereconducted in this embodiment.

FIG. 3(a) is a circuit diagram showing a lumped four parameter modelwhich models the arterial system in the human body.

FIG. 3(b) is a circuit diagram showing a lumped five parameter modelwhich models the arterial system in the human body.

FIG. 4 is a diagram showing the pressure waveform at the left cardiacventricle and the blood pressure waveform at the proximal portion of theaorta.

FIG. 5 is a diagram showing a waveform which models the blood pressurewaveform at the proximal portion of the aorta.

FIG. 6 is a flow chart showing an overview of the operation of thepulsewave analysis device in this embodiment.

FIG. 7 is a flow chart showing the processing operations for parametercalculation in the pulsewave analysis device.

FIG. 8 is a flow chart showing the processing operations for parametercalculation in the pulsewave analysis device.

FIG. 9 is a flow chart showing the processing operations for calculatingα and ω in the pulsewave analysis device.

FIG. 10 is a flow chart showing the processing operations forcalculating ω in the pulsewave analysis device.

FIG. 11 is a waveform diagram showing an example of the waveform at theradius artery obtained through an averaging process in the pulsewaveanalysis device.

FIG. 12 is a waveform diagram showing the superimposition of the radiusartery waveform obtained through calculation processing and the radiusartery waveform obtained through averaging processing in the pulsewaveanalysis device.

FIG. 13 is a diagram for explaining the details of the normalizingprocessing which is applied to the radius artery waveform obtained asresult of averaging processing in the pulsewave analysis device.

FIG. 14 is a diagram showing the correlation between the time t_(s) ofincreasing pressure in the left cardiac ventricle and the time t_(p) ofone beat.

FIG. 15 is a block diagram showing the structure of a pulsewave analysisdevice according to another embodiment of the present invention.

FIG. 16 is a diagram showing the conditions under which measurementsemploying a pulsewave detector 1 were conducted in this embodiment.

FIG. 17 is a diagram showing the display of the superimposition of themeasured and calculated-waveforms of the radius artery, which isdisplayed by output device 6.

FIG. 18 is a squint view of the attachment of a sensor 12 to band 13 ofa wristwatch 11, wherein the compositional elements 10 of the pulse waveanalyzer, excluding sensor 12, are housed in wristwatch 11.

FIG. 19 is a squint view of the attachment of a sensor 22 to the base ofa finger, wherein the compositional elements 10 of the pulse waveanalyzer, excluding sensor 22, are housed in wristwatch 11.

FIG. 20 is a structural diagram showing the attachment of sensor 32 andthe compositional elements 10 of the pulse wave analyzer, excludingsensor 32, to the upper arm via a cuff.

FIG. 21 is a block diagram showing the structure of a sphygmomanometeraccording to the second embodiment of the present invention.

FIG. 22 is a diagram showing the relationship between the pressurewaveform at the aorta (dashed line) and the radius artery waveform(solid line) in a Type I pulsewave.

FIG. 23 is a diagram showing the relationship between the pressurewaveform at the aorta (dashed line) and the radius artery waveform(solid line) in a Type II pulsewave.

FIG. 24 is a diagram showing the relationship between the pressurewaveform at the aorta (dashed line) and the radius artery waveform(solid line) in a Type III pulsewave.

FIG. 25 is a diagram showing the relationship between resistance R_(c)in blood vessels at the center of the arterial system and distortion d.

FIG. 26 is a diagram showing the relationship between resistance R_(p)in blood vessels at the periphery of the arterial system and distortiond.

FIG. 27 is a diagram showing the relationship between inertia L fromblood flow and distortion d.

FIG. 28 is a diagram showing the relationship between compliance C anddistortion d.

FIG. 29 is a diagram for explaining the contraction phase area method.

FIG. 30 is a diagram showing the structure of a sphygmomanometeremploying the conventional technology.

FIG. 31 is a flow chart of the program for obtaining capacitance C_(c).

FIG. 32 is a flow chart of another program for obtaining capacitanceC_(c).

PREFERRED EMBODIMENTS OF THE PRESENT INVENTION

<First Embodiment>

A first embodiment of the present invention will now be explained withreference to the accompanying figures.

FIG. 1 is a block diagram showing the composition of thesphygmomanometer employed in this embodiment. In this embodiment,circulatory state parameters for the arterial system in the human bodyare evaluated based on information obtained from the body usingnon-invasive sensors. The specific details of these circulatory stateparameters will be explained later.

In FIG. 1, a pulsewave detector 1 detects the pulsewave at the radiusartery via a pressure sensor S2 which is attached to the wrist of a testsubject as shown in FIG. 2. Additionally, pulsewave detector 1 detectsthe blood pressure of the test subject via a cuff S1 attached to theupper arm of the subject as shown in FIG. 2. Pulsewave detector 1corrects the measured radius artery pulsewave for blood pressure, andoutputs the result as an analog electric signal. The analog signals areinput to an A/D (analog/digital) converter 3, and are converted todigital signals at a given sampling period.

Stroke-volume measurer 2 is connected to cuff S1 as shown in FIG. 2, andmeasures the stroke volume, i.e., the amount of blood which flows outfrom the heart per beat, via cuff S1. The results of this measurementare output in the form of a digital signal as stroke-volume data. Adevice which carries out measurements using a contraction phase areamethod may be employed for this type of stroke-volume measurer 2.

Microcomputer 4 houses a waveform memory for storing the pulse waveformswhich are taken up from the A/D converter 3, and houses a temporaryrecording memory which is employed as an operational region.Microcomputer 4 carries out the various processing noted below inaccordance with commands which are input from keyboard 5, which is aninput device, and outputs the results obtained from processing to outputdevice 6. The processing steps which follow will be explained in greaterdetail under the explanation of the present invention's operation whichfollows later.

1. Pulsewave readout processing, in which time series digital signals ofthe radius artery waveform obtained via A/D converter 3 are taken up inthe waveform memory (omitted from figures) which housed in microcomputer4.

2. Averaging processing, in which the radius artery waveform taken up inwaveform memory is averaged at each beat, and a radius artery waveform(hereinafter, referred to as “averaged waveform”) corresponding to onebeat is obtained.

3. Uptake processing, in which stroke-volume data is taken up in thetemporary recording memory inside microcomputer 4.

4. Parameter calculation processing, in which an equation expressing theradius artery waveform corresponding to one beat is obtained, and eachof the parameters in an electric model which corresponds to the arterialsystem is calculated based on this equation.

5. First output processing, in which the obtained parameters are outputto output device 6 as circulatory state parameters.

6. Second output processing, in which the pulse waveform at the proximalportion of the aorta is determined from the obtained parameters, thesystolic pressure value, diastolic pressure value, and the heart'sworkload at the proximal portion of the aorta are calculated, and theseresults are output to output device 6.

Output device 6 will now be explained in detail with reference to FIG.1. In this figure, the numeral 61 indicates a measured blood pressuredisplay, which displays systolic and diastolic pressure values actuallymeasured, and the average blood pressure value. 62 is a display fordisplaying the estimated blood pressure value at the center of thearterial system. Display 62 displays average blood pressure E_(0l),systolic pressure E_(m)′, and diastolic pressure E₀ at the center of thearterial system which are obtained as a result of processing which willbe described below. 63 is an alarm display which is composed of aplurality of LEDs which are disposed in a horizontal row. These LEDslight up in response to a difference between the systolic pressureE_(m)′ at the center of the arterial system and the a systolic pressurevalue actually measured. Namely, when the difference between the formerand the latter is less than ±10 mmHg, then a green LED stating “NORMAL”is illuminated. Conversely, when the difference between the former andthe latter exceeds ±10 mmHg, then a red LED stating “CAUTION” isilluminated.

64 is a parameter display. When capacitance C_(c), electrical resistanceR_(c), inductance L, capacitance C, electrical resistance R_(p), timeduration t, of rising pressure in the left cardiac ventricle, timeduration t_(p) of a single beat, stroke volume SV, and workload W_(s)are supplied from microcomputer 4, parameter display 64 displays theseparameters. These parameters will be explained in detail below. 67 is aCRT display for displaying a variety of waveforms, such as the waveformat the radius artery, the pressure waveform at the left cardiacventricle, the pressure waveform of the aorta, and the like. 65 is aprinter which prints out on paper the waveforms displayed on CRT display67 and the various data displayed on measured blood pressure display 61,estimated central blood pressure display 62, warning display 63, andparameter display 64, when print command button 66 is depressed.

The significance of a warning display on warning display 63 will now beexplained.

As explained for FIGS. 22 through 24 previously, there are three typesof differences which may be noted between the systolic pressure valuesof the estimated pressure waveform of the aorta and the radius arterywaveform. When the pulse waveform is a Type I variety (FIG. 22), then itis very likely that the test subject is a healthy individual. On theother hand, test subjects demonstrating Type II or Type III pulsewaveforms are frequently in poor health.

For example, the Type II waveform (FIG. 23) is caused by an anomaly thestate of blood flow, and is highly likely in patients suffering from amammary tumor, liver or kidney ailments, respiratory ailments, stomachor intestinal ailments, inflammation, or the like. The Type IIIwaveform, on the other hand, is caused by an increase in tension in theblood vessel walls, and is very likely in patients having liver or gallailments, dermatological ailments, high blood pressure, or painailments.

Accordingly, the present embodiment provides that a warning display becarried out by means of illuminating a red LED when there is believed tobe an anomaly in the difference between systolic pressure values asdescribed above.

In the preceding example, a diagnosis was made based on the differencebetween the systolic pressure of the pressure waveform at the aorta andthe systolic pressure value of the waveform of the radius artery.However, it is also acceptable to employ the difference in minimum oraverage blood pressure values, instead of the difference in systolicpressure values. Moreover, it is of course acceptable to carry outdiagnosis using the differences in maximum, minimum and average bloodpressure values together.

The present embodiment newly employs a “lumped five parameter model” asan electrical model for the arterial system. There are variouscomponents which determine the behavior of the circulatory system in thehuman body. From among these, the component of aortic compliance hasbeen added to the four parameters of inertia due to blood at the centerof the arterial system, resistance (viscous resistance) in blood vesselsat the center of the arterial system due to blood viscosity, compliance(viscoelasticity) of blood vessels at the periphery of the arterialsystem, and resistance (viscous resistance) in blood vessels at theperiphery of the arterial system, which were employed in the lumped fourparameter model disclosed in Japanese Patent Application Hei 6-205747(Title: Device for Analyzing Pulsewaves), to comprise this lumped fiveparameter model. An electric circuit has been employed to model theseparameters. Additionally, we note here that compliance is a quantityexpressing the degree of pliability of the blood vessels.

FIG. 3(a) shows a circuit diagram for a lumped four parameter model,while FIG. 3(b) shows a circuit diagram for a lumped five parametermodel. The relationship between the parameters and the elements makingup the lumped five parameter model is as follows.

Capacitance C_(c): aortic compliance (cm⁵/dyn)

Electrical resistance R_(c): blood vessel resistance due to bloodviscosity at the center of the arterial system (dyn·s/cm⁵)

Inductance L: inertia of blood at center of arterial system (dyn·s²/cm⁵)

Capacitance C: compliance of blood vessels at periphery of arterialsystem (cm⁵/dyn)

Electrical resistance R_(p): blood vessel resistance at periphery ofarterial system due to blood viscosity (dyn·s/cm⁵)

Currents i, i_(p), i_(c), and i_(s), which are flowing through each partof the electrical circuit, correspond to blood flow (cm³/s). Current iis the blood flow at the aorta and current i_(s) is the blood flowpumped out from the left cardiac ventricle. Input voltage e correspondsto the pressure in the left cardiac ventricle (dyn/cm²), while voltagev_(l) corresponds to the pressure (dyn/cm²) of the proximal portion ofthe aorta. Terminal voltage v_(p) of capacitance C corresponds to thepressure (dyn/cm²) at the radius artery. Further, diode D shown in FIG.3(b) corresponds to the aortic valve. Diode D is on (valve open) duringa period corresponding to contraction, and off (valve closed) during aperiod corresponding to expansion.

As will be explained below, these five parameters are not calculated allat once in the present embodiment. Rather, the lumped four parametermodel disclosed in the reference cited above is employed to calculateall parameters with the exception of capacitance C_(c), after whichcapacitance C_(c) is determined. A theoretical explanation of thebehavior of the lumped four parameter model shown in FIG. 3(a) will nowbe made.

The following differential equation is established for the lumped fourparameter model shown in FIG. 3(a). $\begin{matrix}{v_{1} = {{R_{c}i} + {L\quad \frac{i}{t}} + v_{p}}} & (1)\end{matrix}$

Current i in the above equation may be expressed as: $\begin{matrix}{i = {{i_{c} + i_{p}} = {{C\quad \frac{v_{p}}{t}} + \frac{v_{p}}{R_{p}}}}} & (2)\end{matrix}$

Thus, equation (1) may be rewritten as follows: $\begin{matrix}{v_{1} = {{{LC}\quad \frac{^{2}v_{p}}{t^{2}}} + {\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)\frac{v_{p}}{t}} + {\left( {1 + \frac{R_{c}}{R_{p}}} \right)v_{p}}}} & (3)\end{matrix}$

As is conventionally known, the general solution for a second orderconstant coefficient ordinary differential equation may be obtained bysumming the particular solution (steady-state solution) which satisfiesequation (3) and the transient solution which satisfies the followingdifferential equation. $\begin{matrix}{0 = {{{LC}\quad \frac{^{2}v_{p}}{t^{2}}} + {\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)\frac{v_{p}}{t}} + {\left( {1 + \frac{R_{c}}{R_{p}}} \right)v_{p}}}} & (4)\end{matrix}$

The solution for differential equation (4) is obtained as follows.First, the damped oscillating waveform expressed by the followingequation is assumed as the solution for differential equation (4).

v _(p)=exp(st)  (5)

Substituting equation (5) into equation (4), equation (4) may berewritten as follows. $\begin{matrix}{{\left\{ {{LCs}^{2} + {\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)s} + \left( {1 + \frac{R_{c}}{R_{p}}} \right)} \right\} v_{p}} = 0} & (6)\end{matrix}$

Solving equation (6) for s yields: $\begin{matrix}{s = \frac{{- \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)} \pm \sqrt{\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)^{2} - {4{{LC}\left( {1 + \frac{R_{c}}{R_{p}}} \right)}}}}{2{LC}}} & (7)\end{matrix}$

In equation (7), when $\begin{matrix}{\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)^{2} < {4\quad {{LC}\left( {1 + \frac{R_{c}}{R_{p}}} \right)}}} & (8)\end{matrix}$

then the radicand of the radical sign in the second term becomesnegative, and s is as follows. $\begin{matrix}\begin{matrix}{s = \frac{{- \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)} \pm {j\sqrt{{4{{LC}\left( {1 + \frac{R_{c}}{R_{p}}} \right)}} - \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)^{2}}}}{2{LC}}} \\{= {{- \alpha} \pm {j\quad \omega}}}\end{matrix} & (9)\end{matrix}$

Where, α is the damping factor and ω is the angular frequency.$\begin{matrix}\begin{matrix}{\alpha = \frac{{R_{c}C} + \frac{L}{R_{p}}}{2{LC}}} \\{= \frac{L + {R_{p}R_{c}C}}{2{LCR}_{p}}}\end{matrix} & (10) \\{\omega = \frac{\sqrt{{4{{LC}\left( {1 + \frac{R_{c}}{R_{p}}} \right)}} - \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)^{2}}}{2{LC}}} & (11)\end{matrix}$

Further, when

A ₁ =LC  (12)

$\begin{matrix}{A_{2} = \frac{L + {R_{C}R_{p}C}}{R_{p}}} & (13) \\{A_{3} = \frac{R_{C} + R_{p}}{R_{p}}} & (14)\end{matrix}$

then equations (10) and (11) above may be expressed as follows:$\begin{matrix}{\alpha = \frac{A_{2}}{2A_{1}}} & (15) \\{\omega = \sqrt{\frac{A_{3}}{A_{1}} - \alpha^{2}}} & (16)\end{matrix}$

By confirming the value of s in this way, a solution may be obtainedwhich satisfies differential equation (4). Based on the preceding view,then, equation (5) may be employed as an equation approximating thedamped oscillating component which is included in the response waveformof a the lumped four parameter model.

Next, the pressure waveform at the proximal portion of the aorta will bemodeled. In general, the pressure waveform at the proximal portion ofthe aorta demonstrates a shape as indicated by the heavy line in FIG. 4.In this figure, t_(p) is the time duration of a one beat in a waveform,while t_(s) is the time period during which pressure increases in theleft cardiac ventricle. In a lumped four parameter model, this pressurewaveform is approximated by the triangular wave shown in FIG. 5. Whenthe amplitude and duration of the approximated waveform are indicated asE_(o), E_(m), t_(p), and t_(p1), then the aortic pressure v_(l) at anoptional time t may be expressed by the following equation. Here, E_(o)is the diastolic pressure (blood pressure during expansion phase), E_(m)is the pulse pressure, (E_(o)+E_(m)) is the systolic pressure (bloodpressure during contraction phase), to is the time duration of one beat,and t_(p1) is the time duration from the rise in aortic pressure untilblood pressure falls to a minimum value. In the interval 0≦t<t_(p1):$\begin{matrix}{v_{1} = {E_{o} + {E_{m}\left( {1 - \frac{t}{t_{p1}}} \right)}}} & (17)\end{matrix}$

In the interval t_(p1)≦t<t_(p):

v _(l) =E _(o)  (18)

The response waveform v_(p) (ie., radius artery waveform) when voltagev_(l) which is expressed using equations (17) and (18) is input into theequivalent circuit shown in FIG. 3(a) is as follows.

In the interval 0≦t<t_(p1): $\begin{matrix}{v_{p} = {E_{\min} + {B\left( {1 - \frac{t}{t_{b}}} \right)} + {D_{m1}{\exp \left( {{- \alpha}\quad t} \right)}{\sin \left( {{\omega \quad t} + \theta_{1}} \right)}}}} & (19)\end{matrix}$

In the interval t_(p1)<t≦t_(p):

v _(p) =E _(min) +D _(m2)·exp {−α(t−t _(p1))}·sin {ω(t−t_(p1))+θ₂}  (20)

Here, E_(min) is the diastolic pressure value in the radius arterywaveform which is measured by pulsewave detector 1 (refer to FIG. 11explained below).

The third term from the right in equation (19) and the second term fromthe right in equation (20) are the damped oscillating components inequation (5) explained above. α and ω in these terms may be obtainedfrom equations (15) and (16). B, t_(b), D_(m1), and D_(m2) are constantswhich are calculated in accordance with a procedure described below.

Next, an examination will be made of the constants in equations (19) and(20), with the exception of α and ω which were already confirmed. Tobegin with, the following equation is obtained when equations (17) and(19) are substituted into differential equation (3). $\begin{matrix}\begin{matrix}{{E_{o} + {E_{m}\left( {1 - \frac{t}{t_{p1}}} \right)}} = \quad {{\left( {1 + \frac{R_{c}}{R_{p}}} \right)\left( {E_{\min} + B} \right)} - {\frac{B}{t_{b}}\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)t} +}} \\{\quad \left\{ {{{{LC}\left( {\alpha^{2} - \omega^{2}} \right)}D_{m1}} - {\alpha \quad {D_{m1}\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)}} +} \right.} \\{{\left. \quad {D_{m1}\left( {1 + \frac{R_{c}}{R_{p}}} \right)} \right\} \times {\exp \left( {{- \alpha}\quad t} \right)}{\sin \left( {{\omega \quad t} + \theta_{1}} \right)}} +} \\{\quad \left\{ {{\omega \quad {D_{m1}\left( {{R_{c}C} + \frac{L}{R_{p}}} \right)}} - {2{LC}\quad {\alpha\omega}\quad D_{m1}}} \right\}} \\{\quad {{\exp \left( {{- \alpha}\quad t} \right)}\cos \quad \left( {{\omega \quad t} + \theta_{1}} \right)}}\end{matrix} & (21)\end{matrix}$

The following conditions are necessary in order to establish thepreceding equation (21). $\begin{matrix}\begin{matrix}{{E_{o} + E_{m}} = {\left( {1 + \frac{R_{c}}{R_{p}}} \right)\left( {E_{\min} + B} \right)}} \\{= {E_{o} + {A_{3}B} - {\frac{B}{t_{b}}\quad A_{2}}}}\end{matrix} & (22) \\{\frac{E_{m}}{t_{p1}} = {{\frac{B}{t_{b}}\left( {1 + \frac{R_{c}}{R_{p}}} \right)} = \frac{A_{3}B}{t_{b}}}} & (23) \\{{{{LC}\left( {\alpha^{2} - \omega^{2}} \right)} - {\alpha \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)} + \left( {1 + \frac{R_{c}}{R_{p}}} \right)} = 0} & (24) \\{{{R_{c}C} + \frac{L}{R_{p}}} = {2{LC}\quad \alpha}} & (25)\end{matrix}$

Equations (24) and (25) restrict α and ω, however, these equations aresatisfied by α and ω as obtained according to equations (15) and (16)above.

When equations (18) and (20) are substituted into differential equation(3), the following equation is obtained. $\begin{matrix}\begin{matrix}{E_{o} = \quad {{\left( {1 + \frac{R_{c}}{R_{p}}} \right)E_{\min}} + \left\{ {{{{LC}\left( {\alpha^{2} - \omega^{2}} \right)}D_{m2}} -} \right.}} \\{{\quad \left. {{\alpha \quad \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)D_{m2}} + {\left( {1 + \frac{R_{c}}{R_{p}}} \right)D_{m2}}} \right\}} \times} \\{\quad {{\left. {\exp\left( {- {\alpha\left( \quad {t - t_{p1}} \right)}} \right.} \right\} \sin \quad \left. \left( {{\omega \quad \left( {t - t_{p1}} \right)} + \theta_{2}} \right. \right\}} +}} \\{\quad {\left\{ {{\omega \quad \left( {{R_{c}C} + \frac{L}{R_{p}}} \right)D_{m2}} - {2{LC}\quad {\alpha\omega}\quad D_{m2}}} \right\} \times}} \\{\quad {\left. {\exp\left( {- {\alpha\left( \quad {t - t_{p1}} \right)}} \right.} \right\} \cos \quad \left. \left( {{\omega \quad \left( {t - t_{p1}} \right)} + \theta_{2}} \right. \right\}}}\end{matrix} & (26)\end{matrix}$

In addition to equations (24) and (25), it is also necessary to set upthe following equation in order to establish equation (26).$\begin{matrix}{E_{o} = {{\left( {1 + \frac{R_{c}}{R_{p}}} \right)E_{\min}} = {A_{3}E_{\min}}}} & (27)\end{matrix}$

Next, each of the constants in equations (19) and (20) will becalculated based on conditional equations (22) through (25) and (27) forsetting up differential equation (3).

First, the following equation is obtained for E_(min) from equation(27). $\begin{matrix}{E_{\min} = \frac{E_{O}}{A_{3}}} & (28)\end{matrix}$

An equation for B is obtained from equation (23): $\begin{matrix}{B = \frac{t_{b}E_{m}}{t_{p1}A_{3}}} & (29)\end{matrix}$

When equation (29) is substituted into equation (22), and solved fort_(b), the following equation is obtained: $\begin{matrix}{t_{b} = \frac{{t_{p1}A_{3}} + A_{2}}{A_{3}}} & (30)\end{matrix}$

Next, values are selected for the remaining constants D_(m1), D_(m2),θ₁, and θ₂ so that radius artery waveform v_(p) remains continuous overt=0, t_(p1), t_(p), i.e. values are selected which satisfy the followingconditions a through d.

a. v_(p)(t_(p1)) in equation (19) and v_(p)(t_(p1)) in equation (20) areequivalent

b. v_(p)(t_(p)) in equation (20) and v_(p)(0) in equation (19) areequivalent

c. The differential coefficients at t=t_(p1) in equations (19) and (20)are equivalent

d. The differential coefficient of equation (19) at t=0 and thedifferential coefficient of equation (20) at t=t_(p) are equivalent

In other words, values are selected for D_(m1) and θ₁ so that:$\begin{matrix}{D_{m1} = \frac{\sqrt{D_{11}^{2} + D_{12}^{2}}}{\omega}} & (31) \\{\theta_{1} = {\tan^{- 1}\quad \frac{D_{11}}{D_{12}}}} & (32)\end{matrix}$

where,

D ₁₁=(v _(o1) −B−E _(min))ω  (33)

$\begin{matrix}{D_{12} = {{\left( {v_{O1} - B - E_{\min}} \right)\alpha} + \frac{B}{t_{p}} + \frac{i_{O1}}{C}}} & (34)\end{matrix}$

and v_(o1) and i_(o1) are the initial values of v_(p) and i_(c) at t=0.

Further, values are selected for D_(m2) and θ₂ so that: $\begin{matrix}{D_{m2} = \frac{\sqrt{D_{21}^{2} + D_{22}^{2}}}{\omega}} & (35) \\{\theta_{2} = {\tan^{- 1}\quad \frac{D_{21}}{D_{22}}}} & (36)\end{matrix}$

where,

 D ₂₁=(v _(o2)−E_(min))·ω  (37)

$\begin{matrix}{D_{22} = {{\left( {v_{O2} - E_{\min}} \right) \cdot \alpha} + \frac{i_{O2}}{C}}} & (38)\end{matrix}$

and v_(o2) and i_(o2) are the initial values of v_(p) and i_(c) att=t_(p1).

In this manner, then, each of the constants in equations (19) and (20)are obtained.

Next, the following equation for blood vessel resistance R_(c) isobtained by means of an inverse operation from angular frequency ω inequation (16). $\begin{matrix}{R_{C} = \frac{L - {2R_{p}\sqrt{{LC}\left( {1 - {\omega^{2}{LC}}} \right)}}}{{CR}_{p}}} & (39)\end{matrix}$

Here, the condition for R_(c) to be a real and positive number is:$\begin{matrix}{\frac{4\quad R_{p}^{2}C}{1 + \left( {2\quad \omega \quad R_{p}C} \right)^{2}} \leqq L \leqq \frac{1}{\omega^{2}C}} & (40)\end{matrix}$

In general, R_(p) and C are on the order of 10³[dyn·s/cm⁵] and10⁻⁴[cm/⁵/dyn], respectively. ω may be viewed to be on the order of 10(rad/s) or greater, since it is the angular frequency of the oscillationcomponent which is superimposed on the pulsewave. For this reason, thelower limit of equation (40) is viewed to be around 1/(ω²C).Accordingly, when L is approximated by the following equation (41) forthe purposes of simplification $\begin{matrix}{L = \frac{1}{\omega^{2}C}} & (41)\end{matrix}$

R_(c) becomes: $\begin{matrix}{R_{C} = \frac{L}{{CR}_{p}}} & (42)\end{matrix}$

From the relationship between equations (41) and (42), the dampingconstant α in equation (15) becomes: $\begin{matrix}{\alpha = \frac{1}{{CR}_{p}}} & (43)\end{matrix}$

Using the relationships between equations (41) through (43), theremaining parameters in the lumped four parameter model may be expressedusing α, ω, and L as follows. $\begin{matrix}{R_{p} = \frac{\omega^{2}L}{\alpha}} & (45) \\{C = \frac{1}{\omega^{2}L}} & (46)\end{matrix}$

Thus, it is clear that the parameters are confirmed by obtaining α, ωand L from the preceding equations (44) through (46).

α, ω, B and t_(b) may be obtained from the actual measured waveform atthe radius artery, and L can be calculated based on the stroke volumeSV, as will be explained below. The process for calculating L based onstroke volume SV will now be explained.

First, the average value E_(0l) of the pressure wave at the proximalportion of the aorta is obtained from the following equation.$\begin{matrix}{E_{01} = \frac{{E_{o}t_{p}} + \frac{t_{p1}E_{m}}{2}}{t_{p}}} & (47)\end{matrix}$

The following equation may be established between R_(c), R_(p), α, ω,and L. $\begin{matrix}{{R_{c} + R_{p}} = {{{\alpha \quad L} + \frac{\omega^{2}L}{\alpha}} = {\left( {\alpha^{2} + \omega^{2}} \right)\frac{L}{\alpha}}}} & (48)\end{matrix}$

The result of dividing the average current i.e., average value E_(0l),flowing through the lumped four parameter model by (R_(c)+R_(p))corresponds to the average value (SV/t_(p)) of blood flow flowingthrough the arteries due to the pulse. Accordingly, the followingequation may be established. $\begin{matrix}{\frac{SV}{t_{p}} = {\frac{\alpha}{\left( {\alpha^{2} + \omega^{2}} \right)L}\quad \frac{1}{t_{p}}\quad \left( {{E_{o}t_{p}} + \frac{t_{p1}E_{m}}{2}} \right)}} & (49)\end{matrix}$

By solving the thus-obtained equation 49 for L, an equation forobtaining L from stroke volume SV may be obtained as follows.$\begin{matrix}{L = {\alpha \cdot \frac{{E_{o}t_{p}} + \frac{t_{p1}E_{m}}{2}}{\left( {\alpha^{2} + \omega^{2}} \right){SV}}}} & (50)\end{matrix}$

The value corresponding to average current(1/t_(p)){E₀t_(p)+t_(p1)E_(m)/2)} in equation (49) may be obtained bymeasuring the blood flow volume, and inductance L may be calculatedbased on this result. As a device for measuring blood flow volume, thereare available devices employing the inductance method, the Dopplermethod and the like In the case of a device which measures blood rateusing the Doppler method, there are available devices employingsupersonic waves and laser.

Next, a theoretical explanation will be made of the method forcalculating the circulatory state parameters based on a lumped fiveparameter model. As mentioned before, the circulatory state parametersR_(c), R_(p), C, and L are determined using a lumped four, parametermodel. Accordingly, the value of capacitance C_(c) is determined basedon these parameters. It is therefore necessary to obtain current i,current i_(s), voltage v₁, and voltage v_(p) in FIG. 3(b).

First, the pressure waveform at the left cardiac ventricle isapproximated with a sinusoidal wave such as shown in FIG. 4. In otherwords, by setting ω_(s)=π/t_(s), the pressure waveform e of the leftcardiac ventricle is expressed by the following equation.

e=E′ _(m) sin ω_(s) t  (51)

Here E_(m)′ is the systolic pressure and, if stated in terms of FIG. 5,corresponds to (E_(m)+E₀).

An explanation will now be made, taking the cases where time duration tcorresponds to the contraction phase of t₁≦t<t₂ and to the expansionphase t₂≦t<(t_(p)+t₁), as shown in FIG. 4. Here, time t₁ and time t₂ arethe times at which the pressure waveform of the left cardiac ventriclewaveform and the pressure waveform of the aorta intersect.

(Contraction Phase)

In this case, the equation v₁=e, as well as equations (1) and (2) forvoltage v₁ and current i, respectively, are established. Accordingly,the following differential equation is set up from equations (1) through(3), (12) through (14) and (51). $\begin{matrix}{{{A_{1}\quad \frac{^{2}v_{p}}{t^{2}}} + {A_{2}\quad \frac{v_{p}}{t}} + {A_{3}v_{p}}} = {E_{m}^{\prime}\sin \quad \omega_{s}t}} & (52)\end{matrix}$

First, in the same manner as the lumped four parameter model, thesteady-state solution V_(pst) for this differential equation isobtained. For this purpose, the following equation is assumed for thesteady-state solution V_(pst).

v _(pst) =E ₁ cos ω_(s) t+E ₂ sin ω_(s) t  (53)

By comparing the coefficients by substituting equation (53) for the termv_(p) in equation (52), the following two equations are obtained.

(A ₃·ω_(s) ² A ₁) E₁+ω_(s) A ₂ E ₂=0  (54)

 −ω_(s) A ₂ E ₁+(A ₃−ω_(s) ² A ₁)E ₂ =E _(m′)  (55)

Solving these equations, the following equations (56) and (57) areobtained. $\begin{matrix}{E_{1} = \frac{{- \omega_{s}}A_{2}E_{m}^{\prime}}{\left( {\omega_{s}A_{2}} \right)^{2} + \left( {A_{3} - {\omega_{s}^{2}A_{1}}} \right)^{2}}} & (56) \\{E_{2} = \frac{\left( {A_{3} - {\omega_{s}^{2}A_{1}}} \right)E_{m}^{\prime}}{\left( {\omega_{s}A_{2}} \right)^{2} + \left( {A_{3} - {\omega_{s}^{2}A_{1}}} \right)^{2}}} & (57)\end{matrix}$

Next, the transient solution v_(ptr) for differential equation (52) isobtained. Setting v_(ptr)=exp(λt), this is substituted for v_(p) in thefollowing equation. $\begin{matrix}{{{A_{1}\quad \frac{^{2}v_{p}}{t^{2}}} + {A_{2}\quad \frac{v_{p}}{t}} + {A_{3}v_{p}}} = 0} & (58)\end{matrix}$

As a result, the following equation is obtained.

A ₁λ² +A ₂ λ+A ₃=0  (59)

Solving this equation for λ, the following equation is obtained.$\begin{matrix}\begin{matrix}{\lambda = \frac{{- A_{2}} \pm \sqrt{A_{2}^{2} - {4A_{1}A_{3}}}}{2A_{1}}} \\{= {\left( {- \quad \frac{A_{2}}{2\quad A_{1}}} \right) \pm \sqrt{\left( \frac{A_{2}}{2\quad A_{1}} \right)^{2} - \frac{A_{3}}{A_{1}}}}}\end{matrix} & (60)\end{matrix}$

Setting {A₂/(2A₁)}²<(A₃/A₁) (i.e., oscillation mode), the followingequation is obtained. $\begin{matrix}{\lambda = {{{- \quad \frac{A_{2}}{2\quad A_{1}}} \pm {j\sqrt{\frac{A_{3}}{A_{1}} - \left( \frac{A_{2}}{2\quad A_{1}} \right)^{2}}}} = {{- \beta_{1}} \pm {j\quad \omega_{1}}}}} & (61)\end{matrix}$

In this case, $\begin{matrix}{\beta_{1} = \frac{A_{2}}{2A_{1}}} & (62) \\{\omega_{1} = \sqrt{\frac{A_{3}}{A_{1}} - \beta_{1}^{2}}} & (63)\end{matrix}$

Here, transient solution v_(ptr) is set as in the following equation.

v _(ptr)=(α₁ cos ω₁ t+jα ₂ sin ω₁ t) exp (−β₁ t)  (64)

As a result, voltage v_(p) is expressed as the sum of the steady-statesolution and the transient solution, and therefore may be obtained fromthe following equation using equations (53) and (64).

v _(p)=(E ₁ cos ω_(s) t+E ₂ sin ω_(s) t)+(α₁ cos ω₁ t+jα ₂ sin ω₁ t) exp(−β₁ t)  (65)

The following equation may be obtained for current i by substitutingequation (65) into equation (2). $\begin{matrix}\begin{matrix}{i = \quad {{\left( {\frac{E_{1}}{R_{p}} + {\omega_{s}{CE}_{2}}} \right)\cos \quad \omega_{s}t} + {\left( {{{- \omega_{s}}C_{c}E_{1}} + \frac{E_{2}}{R_{p}}} \right)\sin \quad \omega_{s}t} +}} \\{\quad \left\lbrack {{\left\{ {{\left( \frac{1 - {\beta_{1}{CR}_{p}}}{R_{p}} \right)\cos \quad \omega_{1}t} - {\omega_{1}C\quad \sin \quad \omega_{1}t}} \right\} a_{1}} +} \right.} \\{\left. \quad {j\left\{ {{w_{1}C\quad \cos \quad \omega_{1}t} + {\left( \frac{1 - {\beta_{1}{CR}_{p}}}{R_{p}} \right)\sin \quad \omega_{1}t}} \right\} a_{2}} \right\rbrack {\exp \left( {{- \beta_{1}}t} \right)}}\end{matrix} & (66)\end{matrix}$

Next, the v₀₂ and i₀ are assumed as the values of v_(p) and i,respectively, when t=t₁ as in the followings equations.

i ₀ =J ₀+(α₁ J ₁ +jα ₂ J ₂) exp (−β₁ t ₁)  (67)

v _(o2) =P ₀+(α₁ P ₁ +jα ₂ P ₂) exp (−β₁ t ₁)  (68)

As a result, equations (65) through (68) may be used to establish thefollowing equations. $\begin{matrix}{J_{0} = {{\left( {\frac{E_{1}}{R_{p}} + {\omega_{s}{CE}_{2}}} \right)\cos \quad \omega_{s}t_{1}} + {\left( {{{- \omega_{s}}{CE}_{1}} + \frac{E_{2}}{R_{p}}} \right)\sin \quad \omega_{s}t_{1}}}} & (69) \\{J_{1} = {{\left( \frac{1 - {\beta_{1}{CR}_{p}}}{R_{p}} \right)\cos \quad \omega_{1}t_{1}} - {\omega_{1}C\quad \sin \quad \omega_{1}t_{1}}}} & (70) \\{J_{2} = {{\omega_{1}C\quad \cos \quad \omega_{1}t_{1}} + {\left( \frac{1 - {\beta_{1}{CR}_{p}}}{R_{p}} \right)\sin \quad \omega_{1}t_{1}}}} & (71)\end{matrix}$

 P ₀ =E ₁ cos ω_(s) t ₁ +E ₂ sin ω_(s) t ₁  (72)

 P ₁=cos ω₁ t ₁  (73)

P ₂=sin ω₁ t ₁  (74)

Next, solving equations (67) and (68) for α₁ and α₂, the followingequations (75) and (76) may be obtained. $\begin{matrix}{a_{1} = {\left\{ \frac{{\left( {v_{02} - P_{0}} \right)J_{2}} - {\left( {i_{0} - J_{0}} \right)P_{2}}}{{J_{2}P_{1}} - {J_{1}P_{2}}} \right\} {\exp \left( {\beta_{1}t_{1}} \right)}}} & (75) \\{a_{2} = {\left\{ \frac{{{- \left( {v_{02} - P_{0}} \right)}J_{1}} + {\left( {i_{0} - J_{0}} \right)P_{1}}}{j\left( {{J_{2}P_{1}} - {J_{1}P_{2}}} \right)} \right\} {\exp \left( {\beta_{1}t_{1}} \right)}}} & (76)\end{matrix}$

Next, the relationship expressed by the following equation may beestablished from equations (70) through (74).

J ₂ P ₁ −J ₁ P ₂=ω₁ C  (77)

Accordingly, when equations (75) and (76) are substituted into equation(64), and equation (77) is employed, then the following equation isobtained as transient solution v_(ptr). $\begin{matrix}\begin{matrix}{v_{ptr} = \quad \left\lbrack {{\left( {v_{02} - P_{0}} \right)\cos \quad {\omega_{1}\left( {t - t_{1}} \right)}} -} \right.} \\{\left. \quad \frac{\left\{ {{\left( {1 - {\beta_{1}{CR}_{p}}} \right)\left( {v_{02} - P_{0}} \right)} - {R_{p}\left( {i_{0} - J_{0}} \right)}} \right\} \left\{ {\sin \quad {\omega_{1}\left( {t - t_{1}} \right)}} \right\}}{\omega_{1}{CR}_{p}} \right\rbrack \times} \\{\quad {{\exp \left( {\beta_{1}t_{1}} \right)}{\exp \left( {{- \beta_{1}}t} \right)}}}\end{matrix} & (78)\end{matrix}$

Where, when

 B _(1tr) =v ₀₂ −P ₀  (79)

t′=t−t ₁  (80)

$\begin{matrix}{B_{2{tr}} = {- \quad \frac{{\left( {1 - {\beta_{1}{CR}_{p}}} \right)\left( {v_{02} - P_{0}} \right)} - {R_{p}\left( {i_{0} - J_{0}} \right)}}{\omega_{1}{CR}_{p}}}} & (81)\end{matrix}$

then the following equation (82) is obtained.

v _(ptr)=(B _(1tr) cos ω₁ t′+B _(2tr) sin ω₁ t′) exp (−β₁ t′)  (82)

Accordingly, equation (65) becomes as follows.

v _(p)=(E ₁ cos ω_(s) t+E ₂ sin ω_(s) t)+(B _(1tr) cos ω₁ t′+B _(2tr)sin ω₁ t′) exp (−β₁ t′)  (83)

Next, the terms in the above equation (66) are defined as follows:$\begin{matrix}{D_{1{st}} = {\frac{E_{1}}{R_{p}} + {\omega_{s}{CE}_{2}}}} & (84) \\{D_{2{st}} = {{{- \omega_{s}}{CE}_{1}} + \frac{E_{2}}{R_{p}}}} & (85) \\{D_{1{tr}} = {{\left( \frac{1 - {\beta_{1}{CR}_{p}}}{R_{p}} \right)B_{1{tr}}} + {\omega_{1}{CB}_{2{tr}}}}} & (86) \\{D_{2{tr}} = {{{- \omega_{1}}{CB}_{1{tr}}} + {\left( \frac{1 - {\beta_{1}{CR}_{p}}}{R_{p}} \right)B_{2{tr}}}}} & (87)\end{matrix}$

As a result, the following equation (88) is obtained for current i:

i=(D _(1st) cos ω_(s) t+D _(2st) sin ω_(s) t)+(D _(1tr) cos ω₁ t′+D_(2tr) sin ω₁ t′) exp (−≢₁ t′)  (88)

Current i_(s) is obtained as the following equation. $\begin{matrix}{i_{s} = {{{C_{c}\quad \frac{v_{1}}{t}} + i} = {{\omega_{s}C_{c}E_{m}^{\prime}\cos \quad \omega_{s}t} + i}}} & (89)\end{matrix}$

(Expansion Phase)

During expansion, diode D turns OFF, ending the impression of the leftcardiac ventricle pressure e on the cathode side of the diode D circuit.As a result, the current flowing through capacitance C_(c) has the sameabsolute value and the opposite polarity of current i. Accordingly,voltage v₁ may be expressed by the above equation (1), while currents iand i_(c) may be expressed by the following equations, respectively.$\begin{matrix}{i = {{- C_{c}}\quad \frac{v_{1}}{t}}} & (90) \\{i_{c} = {C\quad \frac{v_{p}}{t}}} & (91)\end{matrix}$

Accordingly, voltage v_(p) becomes $\begin{matrix}{v_{p} = {{R_{p}\left( {i - i_{c}} \right)} = {- {R_{p}\left( {{C_{c}\quad \frac{v_{1}}{t}} + {C\quad \frac{v_{p}}{t}}} \right)}}}} & (92)\end{matrix}$

Further, since i−ic=i_(p)=v_(p)/R_(p), the following equation results.$\begin{matrix}{i = {\frac{v_{p}}{R_{p}} + {C\quad \frac{v_{p}}{t}}}} & (93)\end{matrix}$

Substituting equation (93) into equation (1), and differentiating bothsides of the obtained equation with respect to time t, the followingequation is obtained. $\begin{matrix}{\frac{v_{1}}{t} = {{{LC}\quad \frac{^{3}v_{p}}{t^{3}}} + {\left( {\frac{L}{R_{p}} + {CR}_{c}} \right)\frac{^{2}v_{p}}{t^{2}}} + {\left( {\frac{R_{c}}{R_{p}} + 1} \right)\frac{v_{p}}{t}}}} & (94)\end{matrix}$

Next, the following equation may be drawn from equations (90) and (93).$\begin{matrix}{\frac{v_{1}}{t} = {- \quad \frac{\frac{v_{p}}{R_{p}} + {C\quad \frac{v_{p}}{t}}}{C_{c}}}} & (95)\end{matrix}$

Further, the following equation may be obtained from equations (94) and(95). $\begin{matrix}{{{{LC}\quad \frac{^{3}v_{p}}{t^{3}}\left( \frac{L + {{CR}_{c}R_{p}}}{R_{p}} \right)\frac{^{2}v_{p}}{t^{2}}} + {\left( \frac{{C_{c}R_{c}} + {C_{c}R_{p}} + {CR}_{p}}{C_{c}R_{p}} \right)\frac{v_{p}}{t}} + {\left( \frac{1}{C_{c}R_{p}} \right)v_{p}}} = 0} & (96)\end{matrix}$

Accordingly, the is equation may be restarted as: $\begin{matrix}{{\frac{^{3}v_{p}}{t^{3}} + {A_{1}^{\prime}\quad \frac{^{2}v_{p}}{t^{2}}} + {A_{2}^{\prime}\quad \frac{v_{p}}{_{t}}} + {A_{3}^{\prime}v_{p}}} = 0} & (97) \\\text{where:} & \quad \\{A_{1}^{\prime} = \frac{L + {{CR}_{c}R_{p}}}{{LCR}_{p}}} & (98) \\{A_{2}^{\prime} = \frac{{C_{c}R_{c}} + {C_{c}R_{p}} + {CR}_{p}}{{LC}_{c}{CR}_{p}}} & (99) \\{A_{3}^{\prime} = \frac{1}{{LC}_{c}{CR}_{p}}} & (100)\end{matrix}$

Next, the following equation is obtained when v_(p)=exp(λt) andsubstituted into equation (97).

(λ³ +A _(1′)λ² +A _(2′) +A _(3′)) exp (λt)=0  (101)

Next, the following definitions are provided. $\begin{matrix}{p = {\frac{A_{1}^{\prime 2}}{9} - \frac{A_{2}^{\prime}}{3}}} & (102) \\{q = {{- \quad \frac{A_{1}^{\prime 3}}{27}} + \frac{A_{1}^{\prime}A_{2}^{\prime}}{6} - \frac{A_{3}^{\prime}}{2}}} & (103)\end{matrix}$

 u=(q+{square root over (q²−p³+L )}) ^(⅓)  (104)

v=(q−{square root over (q²−p³+L )}) ^(⅓)  (105)

$\begin{matrix}{\alpha^{\prime} = {{- \left( {u + v} \right)} + \frac{A_{1}^{\prime}}{3}}} & (106) \\{\beta_{2} = {\frac{u + v}{2} + \frac{A_{1}^{\prime}}{3}}} & (107) \\{\omega_{2} = {\left( {u - v} \right)\quad \frac{\sqrt{3}}{2}}} & (108)\end{matrix}$

 λ₁=−α′  (109)

λ₂=−β₂ +jω ₂  (110)

λ₃=−β₂ −jω ₂  (111)

Note that the oscillation mode is indicated when (q²−p³)>0.

Next, voltage v_(p) is assumed according to the following equation.

v _(p) =b ₁ exp (−α′t)+b ₂ exp {(−β₂ +jω ₂)t}+b ₃ exp {(−β₂ −jω₂)t}  (112)

As a result, current i may be expressed by the following equation aftersubstituting equation (112) into equation (93).

i=g ₀ b ₁ exp (−α′t)+(g ₁ +jg ₂)b ₂ exp {(−β₂ +jω ₂)t}+(g ₁ −jg ₂)b ₃exp {(−β₂ −jω ₂)t}  (113)

where, $\begin{matrix}{g_{0} = \frac{1 - {\alpha^{\prime}{CR}_{p}}}{R_{p}}} & (114) \\{g_{1} = \frac{1 - {\beta_{2}{CR}_{p}}}{R_{p}}} & (115) \\{g_{2} = \frac{\omega_{2}{CR}_{p}}{R_{p}}} & (116)\end{matrix}$

Accordingly, voltage v_(i) becomes as follows from equation (113).$\begin{matrix}\begin{matrix}{v_{1} = \quad {{- \quad \frac{1}{C_{C}}}{\int{i{t}}}}} \\{= \quad {{f_{0}b_{1}{\exp \left( {{- \alpha^{\prime}}t} \right)}} + {\left( {f_{1} + {j\quad f_{2}}} \right)b_{2}\exp \left\{ {\left( {{- \beta_{2}} + {j\omega}_{2}} \right)t} \right\}} +}} \\{\quad {\left( {f_{1} - {j\quad f_{2}}} \right)b_{3}\exp \left\{ {\left( {{- \beta_{2}} - {j\omega}_{2}} \right)t} \right\}}}\end{matrix} & (117) \\\text{where,} & \quad \\{f_{0} = \frac{g_{0}}{\alpha^{\prime}C_{c}}} & (118) \\{f_{1} = \frac{{\beta_{2}g_{1}} - {\omega_{2}g_{2}}}{\left( {\beta_{2}^{2} + \omega_{2}^{2}} \right)C_{c}}} & (119) \\{f_{2} = \frac{{\omega_{2}g_{1}} + {\beta_{2}g_{2}}}{\left( {\beta_{2}^{2} + \omega_{2}^{2}} \right)C_{c}}} & (120)\end{matrix}$

Next, for the purpose of simplifying calculations, time t₂ shown in FIG.4 will be set to t=0. When voltage v₁, voltage v_(p) and current i att=0 are set respectively to v₀₁, v₀₂ and i₀, then the followingexpressions are obtained when the term t in equations (117), (112) and(113) is set to t=0.

v₀₁ =f ₀ b ₁+(f ₁ +jf ₂)b ₂+(f ₁ −jf ₂)b ₃  (121)

v ₀₂ =b ₁ +b ₂ +b ₃  (122)

i ₀ =g ₀ b ₁+(g ₁ +jg ₂)b ₂+(g ₁ −jg ₂)b ₃  (123)

Rewriting the second and third terms in equation (112), the followingequation is obtained for voltage v_(p). $\begin{matrix}\begin{matrix}{v_{p} = \quad {{b_{1}{\exp \left( {{- \alpha^{\prime}}t} \right)}} + \left\{ {{\left( {b_{2} + b_{3}} \right)\cos \quad \omega_{2}t} +} \right.}} \\{{\quad \left. {{j\left( {b_{2} - b_{3}} \right)}\sin \quad \omega_{2}t} \right\}}{\exp \left( {{- \beta_{2}}t} \right)}} \\{= \quad {{B_{0}{\exp \left( {{- \alpha^{\prime}}t} \right)}} + {\left( {{B_{1}\cos \quad \omega_{2}t} + {B_{2}\sin \quad \omega_{2}t}} \right){\exp \left( {{- \beta_{2}}t} \right)}}}}\end{matrix} & (124) \\\text{Where,} & \quad \\{B_{0} = {b_{1} = {v_{02} - \frac{{k_{1}g_{2}} - {k_{2}f_{2}}}{{k_{4}g_{2}} - {k_{3}f_{2}}}}}} & (125) \\{B_{1} = {{b_{2} + b_{3}} = \frac{{k_{1}g_{2}} - {k_{2}f_{2}}}{{k_{4}g_{2}} - {k_{3}f_{2}}}}} & (126) \\{B_{2} = {{j\left( {b_{2} - b_{3}} \right)} = \frac{{k_{2}g_{4}} - {k_{1}f_{3}}}{{k_{4}g_{2}} - {k_{3}f_{2}}}}} & (127)\end{matrix}$

and

k ₁ =v ₀₁ −f ₀ v ₀₂  (128)

k ₂ =i ₀ −g ₀ v ₀₂  (129)

k ₃ =g ₁ −g ₀  (130)

k ₄ =f ₁ −f ₀  (131)

Next, the following equation is obtained for current i by substitutingv_(p) of equation (124) into equation 2.

i D ₀ exp (−α′t)+(D ₁ cos ω₂ t) exp (−β₂ t)  (132)

Where, $\begin{matrix}{D_{0} = {\left( \frac{1 - {\alpha^{\prime}{CR}_{p}}}{R_{p}} \right)B_{0}}} & (133) \\{D_{1} = {{\left( \frac{1 - {\beta_{2}{CR}_{p}}}{R_{p}} \right)B_{1}} + {\omega_{2}{CB}_{2}}}} & (134) \\{D_{2} = {{{- \omega_{2}}{CB}_{1}} + {\left( \frac{1 - {\beta_{2}{CR}_{p}}}{R_{p}} \right)B_{2}}}} & (135)\end{matrix}$

Accordingly, from equation (132), voltage v₁ becomes: $\begin{matrix}\begin{matrix}{v_{1} = \quad {{- \quad \frac{1}{C_{C}}}{\int{i{t}}}}} \\{= \quad {{H_{0}{\exp \left( {{- \alpha^{\prime}}t} \right)}} + {\left( {{H_{1}\cos \quad \omega_{2}t} + {H_{2}\sin \quad \omega_{2}t}} \right){\exp \left( {{- \beta_{2}}t} \right)}}}}\end{matrix} & (136) \\\text{Where,} & \quad \\{H_{0} = \frac{D_{0}}{\alpha^{\prime}C_{c}}} & (137) \\{H_{1} = \frac{{\beta_{2}D_{1}} + {\omega_{2}D_{2}}}{\left( {\beta_{2}^{2} + \omega_{2}^{2}} \right)C_{c}}} & (138) \\{H_{2} = \frac{{{- \omega_{2}}D_{1}} + {\beta_{2}D_{2}}}{\left( {\beta_{2}^{2} + \omega_{2}^{2}} \right)C_{c}}} & (139)\end{matrix}$

In the preceding explanation, time t₂ was set to t=0. Therefore, asubstitution of t→(t−t₂) is carried out in order to match the timescale. Voltage v₁, voltage v_(p) and current i can be obtained asfollows from equations (136), (124) and (132) respectively.$\begin{matrix}\begin{matrix}{v_{1} = \quad {{H_{0}\exp \left\{ {- {\alpha^{\prime}\left( {t - t_{2}} \right)}} \right\}} + \left\{ {{H_{1}\cos \quad {\omega_{2}\left( {t - t_{2}} \right)}} +} \right.}} \\{{\quad \left. {H_{2}\sin \quad {\omega_{2}\left( {t - t_{2}} \right)}} \right\}}\exp \left\{ {- {\beta_{2}\left( {t - t_{2}} \right)}} \right\}} \\{= \quad {{H_{0}\exp \left\{ {- {\alpha^{\prime}\left( {t - t_{2}} \right)}} \right\}} +}} \\{\quad {\left\lbrack {H_{m}\sin \quad \left\{ {{\omega_{2}\left( {t - t_{2}} \right)} + \varphi_{21}} \right\}} \right\rbrack \exp \left\{ {- {\beta_{2}\left( {t - t_{2}} \right)}} \right\}}}\end{matrix} & (140) \\\begin{matrix}{v_{p} = \quad {{B_{0}\exp \left\{ {- {\alpha^{\prime}\left( {t - t_{2}} \right)}} \right\}} + \left\{ {{B_{1}\cos \quad {\omega_{2}\left( {t - t_{2}} \right)}} +} \right.}} \\{{\quad \left. {B_{2}\sin \quad {\omega_{2}\left( {t - t_{2}} \right)}} \right\}}\exp \left\{ {- {\beta_{2}\left( {t - t_{2}} \right)}} \right\}} \\{= \quad {{B_{0}\exp \left\{ {- {\alpha^{\prime}\left( {t - t_{2}} \right)}} \right\}} +}} \\{\quad {\left\lbrack {B_{m}\sin \quad \left\{ {{\omega_{2}\left( {t - t_{2}} \right)} + \varphi_{22}} \right\}} \right\rbrack \exp \left\{ {- {\beta_{2}\left( {t - t_{2}} \right)}} \right\}}}\end{matrix} & (141) \\\begin{matrix}{i = \quad {{D_{0}\exp \left\{ {- {\alpha^{\prime}\left( {t - t_{2}} \right)}} \right\}} + \left\{ {{D_{1}\cos \quad {\omega_{2}\left( {t - t_{2}} \right)}} +} \right.}} \\{{\quad \left. {D_{2}\sin \quad {\omega_{2}\left( {t - t_{2}} \right)}} \right\}}\exp \left\{ {- {\beta_{2}\left( {t - t_{2}} \right)}} \right\}} \\{= \quad {{D_{0}\exp \left\{ {- {\alpha^{\prime}\left( {t - t_{2}} \right)}} \right\}} +}} \\{\quad {\left\lbrack {D_{m}\sin \quad \left\{ {{\omega_{2}\left( {t - t_{2}} \right)} + \varphi_{23}} \right\}} \right\rbrack \exp \left\{ {- {\beta_{2}\left( {t - t_{2}} \right)}} \right\}}}\end{matrix} & (142) \\\text{Where,} & \quad \\{H_{m} = \sqrt{H_{1}^{2} + H_{2}^{2}}} & (143) \\{\varphi_{21} = {\tan^{- 1}\quad \frac{H_{1}}{H_{2}}}} & (144) \\{B_{m} = \sqrt{B_{1}^{2} + B_{2}^{2}}} & (145) \\{\varphi_{22} = {\tan^{- 1}\quad \frac{B_{1}}{B_{2}}}} & (146) \\{D_{m} = \sqrt{D_{1}^{2} + D_{2}^{2}}} & (147) \\{\varphi_{23} = {\tan^{- 1}\quad \frac{D_{1}}{D_{2}}}} & (148)\end{matrix}$

Here, current i_(s) during the expansion phase is 0.

Next, a theoretical value for stroke volume SV will be obtained. Strokevolume SV is given by the area of current i_(s) during the contractionphase, and thus may be obtained by integrating equation (89) for currenti_(s) over the range from t₁ to t₂. Namely: $\begin{matrix}\begin{matrix}{{SV} = \quad {\int_{t_{1}}^{t_{2}}{i_{s}{t}}}} \\{= \quad {{\left( \frac{{\omega_{S}C_{C}E_{m}^{\prime}} + D_{1{st}}}{\omega_{S}} \right)\left( {{\sin \quad \omega_{S}t_{2}} - {\sin \quad \omega_{S}t_{1}}} \right)} -}} \\{\quad {{\frac{D_{2{st}}}{\omega_{S}}\left( {{\cos \quad \omega_{S}t_{2}} - {\cos \quad \omega_{S}t_{1}}} \right)} +}} \\{\quad {\frac{\exp \left\{ {- {\beta_{1}\left( {t_{2} - t_{1}} \right)}} \right\}}{\beta_{1}^{2} + \omega_{1}^{2}}\left\{ {{{- \left( {{\beta_{1}D_{1{tr}}} + {\omega_{1}D_{2{tr}}}} \right)}\cos \quad {\omega_{1}\left( {t_{2} - t_{1}} \right)}} +} \right.}} \\{{\quad \left. {\left( {{\omega_{1}D_{1{tr}}} - {\beta_{1}D_{2{tr}}}} \right)\sin \quad {\omega_{1}\left( {t_{2} - t_{1}} \right)}} \right\}} +} \\{\quad \frac{{\beta_{1}D_{1{tr}}} + {{\omega \quad}_{1}D_{2{tr}}}}{\beta_{1}^{2} + \omega_{1}^{2}}}\end{matrix} & (149)\end{matrix}$

An explanation of the operation of the pulsewave analysis deviceaccording to the present embodiment will now be made. FIGS. 6 through 10are flow charts showing the operation of this pulsewave analysis device.FIG. 11 is a waveform diagram of the average waveform which is obtainedas a result of the averaging processing described above. FIG. 12 is awaveform diagram contrasting a radius artery waveform obtained byparameter calculation processing, to be described below, and the averagewaveform which is obtained as a result of averaging. An explanation ofthe pulsewave analysis device's operation now follows, with referencegiven to these figures.

{circle around (1)} Pulsewave Readout Processing

In order to evaluate the circulatory state parameters in a test subject,an diagnostician attaches the cuff S1 and pressure sensor S2 to the testsubject as shown in FIG. 2, and inputs a start-measurement command viakeyboard 5. In response to this command, microcomputer 4 sends anindication to pulsewave detector 1 to measure the pulsewave. As aresult, pulsewave detector 1 detects the radius artery pulsewave, andA/D converter 3 outputs a time-series digital signals showing thisradius artery pulsewave. Microcomputer 4 takes up the digital signals inthe waveform memory housed therein over a fixed interval of time(approximately 1 minute). In this manner, the radius artery waveform fora plurality of beats is taken up in waveform memory.

{circle around (2)} Averaging Processing

Next, at each beat, microcomputer 4 superimposes the radius arterywaveforms over a plurality of beats, and obtains the average waveformper beat over the aforementioned fixed interval of time. Then, thisaverage waveform is stored in the internal memory as a representativewaveform of the radius artery waveforms (Step S1). An example of athus-produced representative waveform WI of the average waveform isshown in FIG. 11.

{circle around (3)} Uptake of Stroke-volume Data Processing

Next, microcomputer 4 sends an indicator to measure stroke volume tostroke-volume measurer 2. As a result, stroke-volume measurer 2 measuresthe stroke volume in the test subject, with the measured result taken upby temporary memory in microcomputer 4 (Step S2).

{circle around (4)} Parameter Calculation Processing

First, the four circulatory state parameter excluding capacitance C_(c)are determined based on the lumped four parameter model.

Processing in microcomputer 4 proceeds to Step S3, executing theparameter calculation processing routine shown in FIGS. 7 and 8. At thistime, the routine shown in FIG. 9 for calculating α and ω is carried out(Steps S109, S117). Accompanying the execution of the routine forcalculating α and ω, the routine for calculating ω shown in FIG. 10 iscarried out (Step S203.)

An explanation will now be made of the details of the processing carriedout in the routines mentioned above. First, as shown in FIG. 11,microcomputer 4 determines for the average waveform of the radius arterythe time t₁′ and blood pressure value y₁ corresponding to a first pointP1 at which blood pressure reaches a maximum value; the time t₂′ andblood pressure value y₂ corresponding to a second point at which bloodpressure falls subsequent to the first point; the time t₃′ and bloodpressure value ye corresponding to a third point P3 which is the secondpeak point; and the time t_(p) per beat and diastolic pressure valueE_(min) (corresponding to the first term in equations (3) and (4) above)(Step S101).

In the case where it is difficult to discriminate between second pointP2 and third point P3 when the pulsewave is gentle, then the times atthe second point and the third point are assumed to be t₂′=2t₁′ andt₃′=3t₁′, respectively.

Next, in order to simplify the processing, normalization of bloodpressure values y₁ to y₃ is carried out using blood pressure value y₀ atpoint A shown in FIG. 13 (Steps S102, S103), and the value at point B isinitially set to (y₀/2)−0.1.

Next, optimal values for B, t_(b), α and ω are determined according tothe following process.

a) B is varied within the range [(y₀/2)˜y₀] and t_(b) is varied withinthe range [(t_(p)/2)˜t_(p)], at +0.1 intervals in both cases. The α andω for which |v_(p)(t₁′)−y₁|, |v_(p)(t₂′)−y₂| and |v_(p)(t₃′)−y₃| areminimized are determined for each B and t_(b).

b) From among the B, t_(b), α and ω values obtained in a) above, the B,t_(b), α and ω for which |v_(p)(t₁′)−y₁|, |v_(p)(t₂′)−y₂ and|v_(p)(t₃′)−y₃| are minimized are determined.

c) Using the B and t_(b) obtained in b) above as standards, theprocessing in a) and b) is carried out again for B within in the rangeof B±0.05 and for t_(b) within the range of t±0.05.

d) When carrying out the processing in a) through c) above, α is variedby 0.1 increments within the range from 3 to 10, and optimal ω valuesare calculated for each α. Next, for each α, dichotomy is used to obtainthe ω at which dv_(p)(t₂′)/dt=0 (see the flow chart in FIG. 10). Whencalculating the value of v_(p) in the above processing, the initialvalue v₀₁ in equation (33) is set to zero. As a result of the precedingprocessing, the final values of B, t_(b), α and ω are determined.

e) t_(p1), E_(m), and E₀ are calculated based on equations (28) through(30) and (44) through (46) (Steps S123, S124).

f) The value of L is calculated based on the measured stroke volume,using equation (50) (Step S125), and the remaining parameters R_(c),R_(p), and C are obtained from equations (44) through (46) (Step S126).

Next, based on the lumped five parameter model, the final circulatoryparameter of capacitance C_(c) is determined. For this purpose, methodsmay be considered wherein capacitance C_(c) is determined so that thecalculated value and the actual measured value of stroke volume SV areequivalent, and wherein capacitance C_(c) is determined so that thecalculated value and the actual measured value of the diastolic pressureof the pulsewave are equivalent. Each of these methods will be explainedseparately.

{circle around (4)}-1. Method to Determine Capacitance C_(c) (AorticCompliance) so that the Calculated and Measured Values of Stroke Volumeare Equivalent

An explanation will first be made of a specific method for determiningcapacitance C_(c) so that the calculated and measured value of strokevolume SV are equivalent.

First, the value of capacitance C_(c) is estimated as in the followingequation, based on the value of capacitance C which was calculated usingthe lumped four parameter model. Moreover, values obtained using thelumped four parameter model are employed for the values of the othercirculatory state parameters, R_(c), R_(p), C and L.

C _(C)=10·C  (150)

Next, stroke volume SV is calculated according to equation (149), usingthese circulatory state parameters. In this case, the time t_(s) ofrising pressure in the left cardiac ventricle is estimated according tothe following equation, from the time t_(p) of one beat which wasobtained from the lumped four parameter model.

t _(s)=(1.52−1.079t _(p))t _(p)  (151)

This relational equation is an experimental equation obtained as aresult of measuring the contraction time of the left cardiac ventricleusing a heart echo. As shown in FIG. 14, −0.882 is obtained as thecorrelation coefficient. Additionally, the value obtained using thelumped four parameter model is employed for systolic pressure E_(m)′(see equations (22) and (28)). In addition, time t₁ and t₂ are obtainedfrom the relationship: left cardiac ventricle pressure=aortic pressure.Moreover, since v₀₂ and i₀ are the values of v_(p) and i at t=t₁, t₁ issubstituted for t in equations (83) and (88), to obtain v₀₂ and i₀.

The value of capacitance C_(c) is determined so that the calculatedvalue for stroke volume SV obtained as above is equivalent to themeasured value taken up from stroke-volume measurer 2. In other words,the value of capacitance C_(c) is varied within in a fixed rangestarting from an initial value obtained from equation (150). Then, themeasured value of stroke volume and the value which was calculated fromeach capacitance C_(c) values is compared, and a check is made to see ifthe integer part of the measured and calculated values are equivalent.If the integer parts are equivalent, then the measured and calculatedvalues of capacitance are deemed equal, capacitance C_(c) is determined,and parameter calculation processing is terminated.

On the other hand, if no coincidence is observed in the measured andcalculated values of stroke volume merely by adjusting the value ofcapacitance C_(c), then from armong the adjusted capacitance C_(c)values, the capacitance C_(c) value at which the difference between themeasured and calculated values for stroke volume is minimized isselected as the final value for capacitance C_(c). Next, the value ofsystolic pressure E_(m)′ is varied by 1 mmHg within a range of ±3 mmHg,and a check is made for the presence of a coincidence between thecalculated and measured values for stroke volume in the same manner asdescribed above. If a systolic pressure value E_(m)′ is present at whichcoincidence is observed, then that value is set as the final systolicpressure value E_(m)′, and parameter calculation processing isterminated.

If no coincidence is observed between the measured and calculated valuesfor stroke volume even after adjusting the value of systolic pressureE_(m)′, then the value of resistance R_(p) is adjusted. Then, from amongthe adjusted systolic pressure values E_(m)′, the value at which thedifference in the measured and calculated values for stroke volume isminimized is set as the final systolic pressure value E_(m)′. Next,resistance R_(p) is increased or decreased by intervals of10[dyn·s/cm⁵], for example, with the R_(p) value at which the differencebetween the measured and calculated values for stroke volume isminimized selected as the final resistance R_(p) value.

An example of a flow chart for realizing the above-described process isshown in FIG. 31. Note that with respect to the parameters which arevaried within a fixed range in the program, a subscript “v” has beenadded to indicate the original parameters.

{circle around (4)}-2. Method for Determining Capacitance C_(c) so thatthe Diastolic Pressures of the Calculated Pulsewave and the MeasuredPulsewave are Equivalent

Next, an explanation will be made of a method for determiningcapacitance C_(c) so that the diastolic pressures of the calculatedpulsewave and the actual measured pulsewave are equivalent.

In this method, a contraction period QT is first obtained in advancefrom the test subject's electrocardiogram. Next, with respect to thiscontraction period QT, the time t_(s)v during which pressure in the leftcardiac ventricle is rising is varied by intervals of 0.01 secs withinthe range from [QT+0.1(sec)] to [QT+0.2(sec)]. At the same time,systolic pressure E_(m)v′ is varied by intervals of 1 mmHg over therange from [E₀+E_(m)−20 (mmHg)] to [E₀+E_(m)+20 (mmHg)].

In other words, the total number of combinations of each value of timet_(s)v of rising pressure in the left cardiac ventricle and systolicpressure E_(m)v′ is 451. A capacitance C_(c) is calculated for thesecombinations so that the diastolic pressure values of the calculatedpulsewave and the measured pulsewave are equivalent.

Next, the sampling value for the calculated pulsewave in eachcombination is defined as P₁(t) and the sampling value for the actualmeasured pulsewave in each combination is defined as P₂(t), and theaverage deviation ε of the waveform in each combination is obtained fromthe following equation. The capacitance C_(c) (aortic compliance) atwhich this waveform average deviation ε is minimized is employed. Anexample of a flowchart for realizing the above-described process isshown in FIG 32. $\begin{matrix}{ɛ = {\sum\limits_{t = 0}^{t_{p}}\frac{{{P_{2}(t)} - {P_{2}(t)}}}{N}}} & (152)\end{matrix}$

In this manner, then, the circulatory state parameters at which themeasured and calculated values of stroke volume are equivalent are alldetermined.

{circle around (5)} First Output Processing

Once the above-described process for calculating the parameters iscompleted, microcomputer 4 outputs the circulatory state parameters L,C, C_(c), R_(c), and R_(p) to sequential output device 6 (Step S4).

The values of circulatory state parameters calculated from the radiusartery waveform in the case where the test subject is a 32 year old maleare shown below.

Capacitance C_(c) = 0.001213 [cm⁵/dyn] Electric resistance R_(c) =98.768 [dyn·s/cm⁵] Inductance L = 15.930 [dyn·s²/cm⁵] Capacitance C =0.0001241 [cm⁵/dyn] Electric resistance R_(p) = 1300.058 [dyn·s/cm⁵]Time t_(s) of rising pressure in 0.496 [s] left cardiac ventricle = Timet_(p) of one beat = 0.896 [s] Stroke volume SV = 83.6 [cc/beat] Systolicpressure E_(m)' = 117.44 [mmHg]

As shown in FIG. 12, there is good coincidence between the measuredwaveform of the radius artery and the calculated waveform of the radiusartery obtained from the calculated parameters.

{circle around (6)} Second Output Processing

In Step S4, the pressure waveform of the aorta is obtained based on thevalues of the circulatory state parameters L, C, C_(c), R_(c), andR_(p). Namely, by employing equation (51) during the contraction phaseand equation (140) during the expansion phase, the waveform of voltagev₁ is calculated for one beat only (i.e., time 0˜time t_(p) or timet₁˜time (t₁+t_(p))). Then, the calculated waveform is output to outputdevice 6, with the pressure waveform of the aorta displayed. Next, thevalue of the obtained waveform of the proximal portion of the aorta attime t₁ is calculated from these equations, and this calculated value isdefined as the diastolic pressure value E₀. The thus obtained systolicpressure value E_(m)′ is relayed to output device 6 together with thediastolic pressure value, and these values are displayed on outputdevice 6.

Accordingly, by means of the present embodiment, it is possible todisplay each of the circulatory state parameters, as well as thesystolic pressure, diastolic pressure and the pressure waveform of theaorta at the center of the arterial system, for the test subject ordiagnostician.

Further, since equation (51) indicates the pressure waveform at the leftcardiac ventricle, the pressure waveform of the left cardiac ventriclemay be displayed on output device 6 in place of the pressure waveform ofthe aorta, as the pressure waveform at the center of the arterialsystem.

<Embodiment 2>

In the preceding first embodiment, the values of the circulatory stateparameters were calculated from the radius artery waveform and thestroke volume. However, as explained above, in order to carry out adetection of stoke volume, it is necessary to attach cuff S1 to the testsubject, subjecting the subject to some inconvenience. Accordingly, thisembodiment provides for an estimation of blood pressure values at thecenter of the arterial system by focusing attention on a change inaortic pressure based on the shape of the radius artery waveform, andusing distortion to represent the shape of the waveform. In other words,in this embodiment, the circulatory state parameters are derived basedon distortion d which is obtained from the radius artery waveform.

First, in the same manner as in the first embodiment, microcomputer 4carries out {circle around (1)} pulsewave readout and {circle around(2)} averaging, to obtain the average waveform per beat for the radiusartery waveform. Next, a Fourier analysis of the pulsewave is performedby carrying out a fast Fourier transform (FFT) on the average waveform.Next, the fundamental wave's amplitude A₁, the second harmonic wave'samplitude A₂, the third harmonic wave's amplitude A₃, . . . to the nthharmonic wave's amplitude A_(n) are obtained from the frequency spectrumobtained as a result of this analysis. Here, the value of n (which is anatural number) is optimally determined after taking into considerationthe size of the amplitude of the harmonic waves. Based on theseamplitude values, then, distortion d defined by the following equationis calculated. $\begin{matrix}{{{distortion}\quad d} = \frac{\left( {A_{2}^{2} + A_{3}^{2} + \cdots + A_{n}^{2}} \right)^{1/2}}{A_{1}}} & (153)\end{matrix}$

Next, the circulatory state parameters are estimated from the obtaineddistortion d. This estimation is carried out based on the understandingthat there is a correlation in the degree of correspondence between thedistortion of the radius artery waveform and each of the values of thecirculatory state parameters. Namely, distortion d and circulatory stateparameters are measured in advance for a number of test subjects, and arelational equation between distortion and the circulatory stateparameters is derived. Examples of correlations obtained as a result ofmeasuring distortion and the circulatory state parameters R_(c), Rp, Land C are shown in FIGS. 25 through 28. Aortic compliance C_(c) is notshown in these figures, however a correlation coefficient and arelational equation therefor may be obtained in the same manner as forthe other four parameters.

Based on distortion d calculated from the above equation (153) and therelational equations shown in each of FIGS. 25 through 28, thecirculatory state parameters of R_(c), R_(p), L, C, and C_(c) arecalculated. Next, output processing in steps {circle around (5)} and{circle around (6)} of the first embodiment are carried out in the samemanner, to obtain the waveform of one beat of the pressure waveform ofthe aorta from the calculated circulatory state parameters. At the sametime, diastolic pressure value E₀ and systolic pressure value E_(m) atthe proximal portion of the aorta are calculated and displayed on outputdevice 6.

<Embodiment 3>

In this embodiment, in addition to systolic and diastolic pressurevalues at the proximal portion of the aorta, the workload on the heart(hereinafter, referred to as “cardiac workload”) is calculated from theblood pressure waveform at the proximal portion of the aorta which isobtained as described above, and is displayed.

Cardiac workload, one indicator showing the load on the heart, isdefined as the product of stroke volume and aortic pressure, and is theresult of converting stroke volume per minute to workload.

Here, stroke volume is defined as the volume of blood flow sent out fromthe heart at each pulse, and corresponds to the area of the waveform ofblood flow from the heart. Stroke volume is correlated with the area ofcontraction phase of the pressure waveform of the aorta, and may beobtained by applying the contraction phase area method on the pressurewaveform of the aorta.

In other words, the area S under the portion of the pulse waveformcorresponding to a contraction phase in the heart is calculated.Explained in terms of the pulse waveform in FIG. 29, this is the area ofthe region from where the pulsewave is rising to where it notches, asindicated by the hatching. Next, stroke volume SV is calculated usingthe following equation, where K indicates a specific constant.

Stroke volume [ml]=area S [mmHg·s]×K

Cardiac stroke volume is defined as the volume of blood flow sent outfrom the heart per minute. Accordingly, cardiac stroke volume can beobtained by converting stroke volume to minutes. In other words, cardiacstroke volume may be obtained by multiplying stroke volume by heartrate.

In this embodiment, in the output processing in {circle around (5)} ofthe first and second embodiments, microcomputer 4 calculates the cardiacworkload based on the pressure waveform calculated for the left cardiacventricle, and displays this result on output device 6. The otherprocessing is equivalent to the preceding embodiments, and anexplanation thereof will thus be omitted.

Microcomputer 4 calculates cardiac workload W_(s) according to theprocess shown below.

First, w_(s) is defined as the product of e·i_(s), and may be calculatedas follows from equations (51), (88), and (89). $\begin{matrix}\begin{matrix}{w_{s} = \quad {e \cdot i_{s}}} \\{= \quad {{\omega_{s}C_{c}E_{m}^{\prime 2}\sin \quad \omega_{s}t\quad \cos \quad \omega_{s}t} +}} \\{\quad {{E_{m}^{\prime}\sin \quad \omega_{s}{t\left( {{D_{1{st}}\cos \quad \omega_{s}t} + {D_{2{st}}\sin \quad \omega_{s}t}} \right)}} +}} \\{\quad {E_{m}^{\prime}\sin \quad \omega_{s}{t\left( {{D_{1{tr}}\cos \quad \omega_{1}t} + {D_{2{tr}}\sin \quad \omega_{1}t}} \right)}{\exp \left( {{- \beta_{1}}t^{\prime}} \right)}}}\end{matrix} & (154)\end{matrix}$

Setting the first, second and third terms in equation (154) to w₁, w₂,and w₃, respectively, these terms may be rewritten as follows.$\begin{matrix}{w_{1} = {\frac{\omega_{s}C_{c}E_{m}^{\prime 2}}{2}\quad \sin \quad 2\quad \omega_{s}t}} & (155) \\{{w_{2} = {\frac{E_{m}^{\prime}}{2}\quad \left\{ {{D_{1{st}}\sin \quad 2\omega_{2}t} - {D_{2{st}}\left( {{\cos \quad 2\quad \omega_{s}t} - 1} \right)}} \right\}}}\quad} & (156) \\\begin{matrix}{w_{3} = \quad {\frac{E_{m}^{\prime}}{2}\quad\left\lbrack {{D_{1{tr}}\left\{ {{\sin \quad \left( {{\omega_{s}t} + {\omega_{1}t^{\prime}}} \right)} + {\sin \quad \left( {{\omega_{s}t} - {\omega_{1}t^{\prime}}} \right)}} \right\}} -} \right.}} \\{{\quad \left. {D_{2{tr}}\left\{ {{\cos \quad \left( {{\omega_{s}t} + {\omega_{1}t^{\prime}}} \right)} - {\cos \quad \left( {{\omega_{s}t} - {\omega_{1}t^{\prime}}} \right)}} \right\}} \right\rbrack}{\exp \left( {{- \beta_{1}}t^{\prime}} \right)}}\end{matrix} & (157)\end{matrix}$

Next, using equation (80), the following expressions are defined:

ω_(s) t+ω₁ t′=ω _(s) tω ₁(t−t ₁)=(ω_(s)+ω₁)t−ω ₁ t ₁=ω_(a) t−Φ  (158)

ω_(s) t−ω ₁ t−′=(ω_(s)−ω₁)t+ω ₁ t ₁=ω_(b) t+Φ  (159)

Namely,

ω_(a)=ω_(s)+ω₁  (160)

ω_(b)=ω_(s)−ω₁  (161)

Φ=ω₁ t ₁  (162)

In this case, then, equation (157) becomes as follows: $\begin{matrix}\begin{matrix}{w_{3} = \quad {\frac{E_{m}^{\prime}}{2}\quad\left\lbrack {{D_{1{tr}}\left\{ {{\sin \quad \left( {{\omega_{a}t} - \Phi} \right)} + {\sin \quad \left( {{\omega_{b}t} + \Phi} \right)}} \right\}} -} \right.}} \\{{\quad \left. {D_{2{tr}}\left\{ {{\cos \quad \left( {{\omega_{a}t} - \Phi} \right)} - {\cos \quad \left( {{\omega_{b}t} + \Phi} \right)}} \right\}} \right\rbrack}{\exp \left( {{- \beta_{1}}t^{\prime}} \right)}}\end{matrix} & (163)\end{matrix}$

Next, W₁, W₂, and W₃ are respectively defined as follows, and thefollowing equation is derived from equations (155), (157) and (163).$\begin{matrix}\begin{matrix}{W_{1} = {\int{w_{1}{t}}}} \\{= {{- \quad \frac{C_{c}E_{m}^{\prime 2}}{4}}\quad \cos \quad 2\quad \omega_{s}t}} \\{= {\frac{C_{c}E_{m}^{\prime 2}}{4}\quad \left( {1 - {\cos^{2}\quad \omega_{s}t}} \right)}}\end{matrix} & (164) \\\begin{matrix}{W_{2} = \quad {\int{w_{2}{t}}}} \\{= \quad {\frac{E_{m}^{\prime}}{2}\left\{ {{{- \left( \frac{D_{1{st}}}{2\omega_{s}} \right)}\cos \quad 2\omega_{2}t} - {D_{2{st}}\left( {{\sin \quad \frac{2\quad \omega_{s}t}{2\quad \omega_{s}}} - t} \right)}} \right\}}} \\{= \quad {\left( \frac{E_{m}^{\prime}}{4\quad \omega_{s}} \right)\left\{ {\left( {D_{1{st}} + {2D_{2{st}}\omega_{s}t}} \right) -} \right.}} \\{\quad \left. {2\cos \quad \omega_{s}{t\left( {{D_{1{st}}\cos \quad \omega_{s}t} + {D_{2{st}}\sin \quad \omega_{s}t}} \right)}} \right\}}\end{matrix} & (165) \\\begin{matrix}{W_{3} = \quad {\int{w_{3}{t}}}} \\{= \quad {\frac{E_{m}^{\prime}}{2}\left\{ {\frac{\begin{matrix}{{\left( {{{- \omega_{a}}D_{1{tr}}} + {\beta_{1}D_{2{tr}}}} \right){\cos \left( {{\omega_{a}t} - \Phi} \right)}} -} \\{\left( {{\beta_{1}D_{1{tr}}} + {\omega_{a}D_{2{tr}}}} \right){\sin \left( {{\omega_{a}t} - \Phi} \right)}}\end{matrix}}{\beta_{1}^{2} + \omega_{a}^{2}} +} \right.}} \\{\left. \quad \frac{\begin{matrix}{{{- \left( {{\omega_{b}D_{1{tr}}} + {\beta_{1}D_{2{tr}}}} \right)}{\cos \left( {{\omega_{b}t} + \Phi} \right)}} +} \\{\left( {{{- \beta_{1}}D_{1{tr}}} + {\omega_{b}D_{2{tr}}}} \right){\sin \left( {{\omega_{b}t} + \Phi} \right)}}\end{matrix}}{\beta_{1}^{2} + \omega_{b}^{2}} \right\} {\exp \left( {{- \beta_{1}}t^{\prime}} \right)}}\end{matrix} & (166)\end{matrix}$

Since workload W_(s) is obtained by converting the sum of W₁, W₂, and W₃to a “per minute value,” it may be expressed finally as the followingequation. $\begin{matrix}{W_{s} = {W_{1} + W_{2} + {W_{3} \times 10^{- 7} \times \frac{60}{t_{p}}\quad \text{(J/min)}}}} & (167)\end{matrix}$

The significance of displaying cardiac workload, in addition to systolicand diastolic pressure values at the proximal portion of the aorta, asexplained above is as follows.

Namely, in the conventional sphygmomanometer, blood pressure is measuredat the periphery of the arterial system, such as at the upper arm,radius artery or the like, and is therefore an indirect measurement ofthe load on the heart. However, changes in the load on the heart may notalways be reflected in peripheral blood pressure values. Accordingly,using the periphery of the arterial system to interpret load on theheart cannot be viewed as a method of absolute accuracy.

Accordingly, in the present invention, emphasis is placed on theimportance of using blood pressure waveforms at the center of thearterial system to view cardiac load, with the blood,pressure waveformof the proximal portion of the aorta (i.e., the center of the arterialsystem) estimated from pulse waveforms measured at the periphery. If thesystolic and diastolic pressure values at the proximal portion of theaorta are then calculated from the estimated pressure waveform at theaorta, then these blood pressure values become indicators which directlyshow the load on the heart.

By obtaining cardiac workload as described above based on the pressurewaveform at the aorta, it is possible to provide the systolic anddiastolic pressure values at the proximal portion of the aorta as otheruseful indicators of cardiac load. Therefore, an explanation of theusefulness of cardiac load will now be explained using examples.

First, the case will be considered in which a hypertensive agent isadministered to a patient to treat high blood pressure. Ordinarily, ifthe drug is effective, a change will be noted in the systolic anddiastolic pressure values which are measured at the radius artery.However, even if no change is observed in the systolic and diastolicpressure values, it is still possible that the agent is having an effectin easing the load on the heart. This is because it is not absolutelyessential that a hypertensive agent reduce the blood pressure at theradius artery, but rather, the agent's function is sufficient if itreduces the load on the heart somewhere along the arterial system. Thus,even if no marked change is observed in the blood pressure values at theperiphery of the arterial system, such as at the radius artery, it ispossible to know the actual load on the heart by calculating cardiacworkload which is obtained from the blood pressure waveform at theproximal portion of the aorta.

However, while this type of change in the load on the heart may beobserved by closely examining the blood pressure waveform at theproximal portion of the aorta, it is possible to quantitatively expressvery small changes in the waveform by calculating the cardiac workload.Accordingly, by obtaining cardiac workload and displaying it along withsystolic and diastolic pressure values, it is possible to carry out aneven more precise evaluation of a treatment method employing ahypertensive agent.

The results of calculating cardiac workload for each of the Type Ithrough Type III pulse waveforms are shown in FIGS. 22 through 24.

<Modifications>

The present invention is not limited to the above-described embodiments,but rather a variety of modifications such as those below are alsopossible. For example, a modification may be considered in which thecirculatory state parameters are determined without carrying out ameasurement of stroke volume SV.

Namely, from among the circulatory state parameters in this embodiment,inductance L is defined as a fixed value, and the values of the otherparameters are calculated based only on the waveform of the pulsewavemeasured at the test subject's radius artery. In this case, as shown inFIG. 15, it is possible to omit stroke-volume measurer 2, which one ofthe essential elements in the structure shown in FIG. 1. Accordingly, asshown in FIG. 16, when carrying out measurements in this embodiment,cuff S1, which is required for the measuring arrangement shown in FIG.2, is not necessary.

However, when the value of inductance L is defined as a fixed value, theaccuracy of the obtained circulatory state parameters falls as comparedto a method employing the actual measured value of stroke volume. Thus,in order to compensate for this fact, the waveform W1 of the radiusartery obtained by measurement (i.e., measured waveform) and thewaveform W2 of the radius artery obtained by calculation (i.e.,calculated waveform) are superimposed and displayed on output device 6,as shown in FIG. 17. To begin with, the value of inductance L is definedas the aforementioned fixed value, and a calculated waveform W2 isobtained. This waveform is displayed on output device 6 and the degreeof coincidence with the measured waveform W1 is observed. Next, thediagnostician determines a suitable value which is different from thefixed value to be inductance L. A calculated waveform W2 is againobtained, and the degree of coincidence with measured waveform W1 isobserved on output device 6. Next, the diagnostician suitably determinesa number of values for inductance L in the same manner as describedabove, determines calculated waveforms W2 for each of these inductance Lvalues, and compares each of the calculated waveforms W2 with themeasured waveform W1 on output device 6. One waveform is selected fromamong the calculated waveforms W2 which best matches measured waveformW1, and the value of the associated inductance L at that time isdetermined to be the optimal value.

Additionally, note that when modeling the pressure waveform at theproximal portion of the aorta, a squared-off waveform may be employed inplace of the triangular waveforms described above. In this case, awaveform results which more closely approximately the actual pressurewaveform than where approximating using triangular waves. As a result,it is possible to calculate even more accurate circulatory stateparameters.

Further, the site of measurement of the pulsewave or stroke volume isnot limited to those shown in FIGS. 2 and 16 Rather, any site on thetest subject's body may be used. Namely, in the preceding embodiment,cuff S1 was affixed to the upper arm of the test subject, however, itmay be preferable not to employ a cuff if the convenience of the testsubject is an issue.

Therefore, as one example, an arrangement may be considered in whichboth the radius pulsewave and the stroke volume are measured at thewrist. In this type of design, as shown in FIG. 18, a sensor 12consisting of a sensor for measuring blood pressure and a sensor formeasuring stoke volume are attached to a belt 13 of a wristwatch 11. Atthe same time, structural elements 10 other than sensor 12 of apulsewave analysis device are housed in the main body of wristwatch 11.As shown in the figure, sensor 12 is attached in a freely sliding mannerto belt 13 via a fastener 14. By fastening wristwatch 11 to the wrist ofthe test subject, the sensor presses against the radius artery under asuitable pressure.

In addition, another embodiment may be considered in which the pulsewaveand stroke volume are measured at the finger. An example of thestructure of a device according to this embodiment in shown in FIG. 19.As shown in this figure, a sensor 22 comprising a sensor for measuringblood pressure and a sensor for measuring stroke volume are attached tothe base of a finger (the index finger in this figure). At the sametime, structural elements 10 other than sensor 22 of the pulse waveanalysis device are housed in wristwatch 21 and are attached to sensor22 via lead wires 23,23.

Moreover, by combining these two embodiments, other arrangements may berealized such as one in which the stroke volume is measured at the wristand the pulsewave is measured at the finger, or one in which the strokevolume is measured at the finger and the radius artery pulsewave ismeasured at the wrist.

As in the above-described cases, then, it is possible to realize astructure which does not employ a cuff, so that measurements can becarried out without wrapping an apparatus to the upper arm of the testsubject. Thus, the burden on the test subject during measurement isreduced.

On the other hand, a design such as shown in FIG. 20 may be consideredwhich employs a cuff alone. As shown in this figure, a sensor 32comprising a sensor for measuring blood pressure and a sensor formeasuring stroke volume, and the structural components 10 other thansensor 32 of a pulsewave analysis device are affixed to the upper arm ofa test subject by means of a cuff. Accordingly, a simpler structure ascompared to that in FIG. 2 is realized.

In addition, in the preceding embodiments, the pulsewave was employedwhen calculating circulatory state parameters. However, the presentinvention is not limited thereto; rather other physiological conditionsmay of course be employed for the calculation of the circulatory stateparameters.

What is claimed:
 1. A device for measuring a physiological state in anorganism having an arterial system extending from a center portion ofthe organism's body to a periphery thereof, said device comprising:measuring means for measuring the physiological state on the basis of apulse wave detected at a periphery of the arterial system; and analysismeans for calculating circulatory state parameters, includingviscoelasticity of an aorta of the arterial system, based on themeasured physiological state, to show a circulatory state of thearterial system from the center to the periphery.
 2. A device accordingto claim 1, wherein the circulatory state parameters further includeblood vessel resistance at the center of the arterial system due toblood viscosity, blood inertia at the center of the arterial system,blood vessel resistance at the periphery of the arterial system due toblood viscosity, and blood vessel viscoelasticity at the periphery ofthe arterial system.
 3. A device according to claim 1, furthercomprising blood pressure calculating means for calculating a pressurewaveform at the aorta based on the calculated circulatory stateparameters.
 4. A device according to claim 3, wherein the circulatorystate parameters further include blood vessel resistance at the centerof the arterial system due to blood viscosity, blood inertia at thecenter of the arterial system, blood vessel resistance at the peripheryof the arterial system due to blood viscosity, and blood vesselviscoelasticity at the periphery of the arterial system.